Telescopic wonders of the Starry Heavens. 




1. Great Cluster of Stars in Hercules. 

2. Whirlpool Nebula of Lord Ross. 



A 



COMPENDIUM OF ASTRONOMY; 



CONTAINING- THE 



ELEMENTS OF THE SCIENCE, 

FAMILIARLY EXPLAINED AND ILLUSTRATED, 



ADAPTED TO THE USE OF 



HIGH SCHOOLS AND ACADEMIES, 



AND OF THE 



GENERAL READER. 



A NEW AND GREATLY IMPROVED EDITION, 

CONTAINING THE 

LATEST DISCOVERIES. 



BY DEOTSOK OLMSTED, LL.D., 

PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE. 



fr/**l 



NEW YORK: 

ROBERT B. COLLINS, 254 PEARL-STREET. 

1855. 



Entered according to Act of Congress, in the year 1855, 

By DENIS ON OLMSTED, 

In the Clerk's Office of the District Court of Connecticut. 






.°\ 



N 



PREFACE 



The extensive patronage which this work has enjoyed, both 
as a private manual, and as a text-book in the schools, lays the 
author under peculiar obligation to render it deserving of public 
favor. He has therefore, with much care and pains, prepared 
this revised edition, using his best endeavors to present to the 
learner, in a short compass, a clear, faithful, and comprehensive 
outline of the noble science of Astronomy. The earlier portions 
of the work, treating as they do of subjects which are in their 
nature of a fixed character, such as definitions and the doctrine 
of the sphere, have appeared to him susceptible of little improve- 
ment, and accordingly have been suffered to remain unchanged ; 
but the latter portions, relating to the Planets, Comets, Fixed 
Stars, and Nebulae, have required to be entirely rewritten, in 
order to embrace those numerous and grand discoveries with 
which astronomy has been enriched within a few years past. 

To render difficult subjects plain and intelligible to the young, 
has constituted with him the leading object of a life sedulously 
devoted to the instruction of youth, through the several grada- 
tions of the common-school, the academy, and the university. 
He would not, however, encourage any one to suppose, that he 
can make any valuable attainments in this profound science, 
without diligent study and close reflection. If any book on 
astronomy is very easy, it is because it is very superficial, and 
contains little worth knowing. The riches of this mine lie deep ; 



IV PREFACE. 

and no one can acquire them who is either incompetent or un- 
willing to dive beneath the surface. 

The author would beg leave to direct the attention of teachers 
to the improvements introduced into the present edition for 
learning the Constellations. Although the diagrams here given 
will not supersede the necessity of resorting to the Celestial 
globe, or to maps of the stars, yet as a starting-point they will 
be found greatly to facilitate the study of the nocturnal heavens, 
and to afford to the young learner such plain and conspicuous 
landmarks that he will be able afterwards, with little assistance, 
to travel successively from constellation to constellation, until 
he becomes entirely familiar with every portion of the starry 
firmament. 

Yale College, April, 1855. 



ANALYSIS. 



These Outlines the author has found very valuable as a basis for pub- 
lic examinations. Instead of being interrogated in the usual way by indi- 
vidual questions, the student is assigned at random (or by lot) some portion 
of the Analysis, which, after a little time for collecting his thoughts, he is 
called upon to expand; and the fulness and accuracy with which he per- 
forms this process, determine the mark accorded to him on the scale of 
merit. 



Preliminary Observations. 

PAGE 

Astronomy— defined 1 

Descriptive, Physical, and Practical. 1 
History. Astronomy of the An- 
cients 1 

Astronomy of the Greeks 2 

Pythagoras, Ilipparchus, Ptolemy. . . 2 

Astronomy of the Middle Ages 3 

Copernicus, Tycho Brahe, Kepler, 

Galileo 3 

Astronomy of the Moderns 3 

Sir Isaac Newton, La Place 3 

Astrology — defined 3 

Natural Astrology, Judicial Astrology 3 

Copernican System — briefly stated . 4 

Figure and Dimensions of the 
Earth, and Doctrine of the 
Sphere. 

Figure of the Earth 5 

Proofs of its being globular 5 

Illustrations by Figs. 1 and 2 6 

Exact figure of the earth 6 

Diameter, Circumference 7 

Doctrine of the Sphere— defined . . 8 

Great and small circles 9 

Axis of a circle, pole, secondary 9 

Horizon — sensible and rational 11 

Zenith and Nadir 11 

Vertical Circles, Meridian 12 

Prime Vertical, Altitude, Azimuth, 

Amplitude 12 

Axis of the earth, Poles of the earth 

and heavens 12 

Equator, Hour Circles, Latitude, Lon- 
gitude 13 

Ecliptic, Equinoxes, Solstices, Signs 

of the Zodiac 14 

Colures — equinoctial and solstitial ... 15 

Eight Ascension, Declination 16 

Celestial Latitude and Longitude 16 



PAGE 

Parallels of Latitude, Tropics, Polar 

Circles 16 

Elevation of the Pole in degrees 17 

Elevation of the Equator 17 

Zones — Torrid,Temperate, and Frigid 17 

Zodiac 17 

Huw to represent the Circles of the 

Sphere by an apple 17 

Projection of the Sphere— Fig. 5 19 

Diurnal Revolution. 

Circles of diurnal revolution 21 

Sidereal Day, Eight Sphere, Parallel 

Sphere 22 

Oblique Sphere— Fig. 6 24 

Circle of Perpetual Apparition 25 

Circle of Perpetual Occultation 26 

Artificial Globes— described 2S 

Hour Circles, Hour Index, Quadrant 

of Altitude 30 

To rectify the globe for any place ... 31 
Problems on the Terrestrial Globe . . 31 
To find the Latitude and Longitude 

of a place 31 

To find a place, the Latitude and Lon- 
gitude being given 31 

To find the bearing and distance of 

two places 32 

To determine the difference of time 

in different places 32 

The hour being given at any place, to 
tell what hour it is in any other 

part df the Avorld '. 32 

To find what people live directly un- 
der us 32 

To find what people of the southern 
hemisphere live directly opposite 

to us 32 

To find the Antipodes 33 

To rectify the globe for the Sun's 
place 33 



ANALYSIS. 



PAGE 

The latitude of a place being given, 
to find the time of the Sun's rising 

and setting 34 

Froblems on the Celestial Globe 84 

To find the right ascension and decli- 
nation 34 

To represent the appearance of the 

stars at any time 84 

To find the altitude and azimuth of a 

star 35 

To find the angular distance of two 

stars 35 

To find the sun's meridian altitude. . 35 

Parallax, Refraction, and Twi- 
light. 

Parallax— defined, Fig. 7 86 

Horizontal Parallax— its importance. 37 

Refraction— defined, Fig. 8 33 

Its' amount at different altitudes 40 

Effects of refraction upon the sun and 

moon when near the horizon 41 

Twilight— defined, Fig. 9 42 

Its appearance in different latitudes . 43 

Its uses 44 

Time. 

Time defined 44 

Sidereal day, Solar day 45 

Apparent time, Mean time 46 

Astronomical day, Equation of Time 46 

Clocks, how regulated 46 

The Calendar 47 

Astronomical year, Civil year 47 

Bissextile or Leap-year 48 

Rule for Leap-year 49 

How the common year begins and 

ends 50 

Astronomical Instruments. 

When first used 51 

Angular measurement illustrated ... 52 

Telescope, principle, Fig. 11 53 

Eefractors and Eeflectors 55 

Transit Instrument, Fig. 12 56 

Its use, Noon mark 57 

Astronomical Clock 59 

To what kind of time adapted 59 

Altitude and Azimuth Instrument, 60 

Sextant, Fig. 14 63 

Figure and Density of the Earth. 

Spheroidal figure, Fig. 15 63 

How measured by arcs of the merid- 
ian 66 

By the Pendulum 67 

Difference in the polar and equatorial 

diameters 67 

Earth's ellipticity 67 

Density of the earth 68 

How estimated, Fig. 16 68 



PAGE 

Sun — Solar Spots — Zodiacal 
Light. 

Sun — figure, distance, diameter, size, 

density 70 

Solar Spots— described, Fig. 17 72 

Part of the sun's disk occupied by 

them 72 

Period of their revolution— Extent. . 74 

Zodiacal Light— described, Fig. 20 . 76 

Earth's Annual Motion — Seasons 

— Figure of the Earth's Orbit. 

Annual motion — illustrated, Fig. 21. 79 

Obliquity of the Ecliptic SI 

Apparent motion of the Sun 82 

Dimensions of the Earth's orbit 83 

Seasons — cause of the change of sea- 
sons 84 

Illustration by Fig. 22 85 

Consequences had the ecliptic been 

perpendicular to the equator 86 

Figure of the Earth's Orbit, Fig. 23 8S 
How the variations of the distances 

from the sun are found .- 89 

Universal Gravitation. 

Tendency of all matter to all other 

matter 91 

Illustration by Fig. 24 92 

Law of gravity in'thr ee parts 93 

Law of falling bodies 94 

First law of motion 94 

Universal Gravitation defined 96 

Illustrated by Fig. 25 97 

Kepler's Laws 98 

First law, figure of the planetary or- 
bits 99 

Second law, spaces described by the 

radius vector 101 

Third law, relations between times 

and distances 101 

Motion in an elliptical orbit 102 

Illustrated by Figs. 28, 29, 30 104 

Precession of the Equinoxes 107 

Its annual amount 107 

Tropical year 109 

The Moon. 

Distances, diameter, terminator 110 

Proofs of mountains and valleys 111 

Names of the lunar spots 112 

Heights of lunar mountains 113 

Forms of lunar mountains and val- 
leys 114 

Lunar atmosphere 117 

Whether there is water in the moon. 117 

Whether inhabitants US 

Phases of the moon 120 

Syzygies, quadratures, octants 121 

Phases illustrated by Fig. 81 121 

Revolutions of the moon 122 



ANALYSIS. 



Vll 



P-AGE 

Inclination of the orbit 123 

Why the moon runs high and low .. 124 

Moon's revolution on her axis 125 

Moon's three librations 126 

"Whether the earth carries the moon 

round the sun 128 

Causes of both motions explained. . . 129 

Causes of the lunar irregularities 130 

Figure of the moons orbit 132 

Backward motion of the nodes s 133 

Synodical revolution of the node 133 

The Saros explained 134 

Metonic Cycle 134 

Revolution of the apsides 135 

Periodical and secular irregularities . 135 

Eclipses. 

When an eclipse of the moon happens 137 

When an eclipse of the sun happens. 137 

Illustration by Fig. 32 13S 

Representation, Figs. 33. 34 139 

Why the moon's surface is visible. . . 142 

How eclipses are foretold 143 

Nature of eclipses explained 144 

Annular eclipses 146 

Longitude and Tides. 

How difference of longitude is found 150 

Mode by chronometers 151 

By eclipses 152 

By the lunar method * . 153 

Tides defined 155 

High, low, spring, neap tides 155 

Cause of tides explained 156 

Influence of the declination of the sun 

and moon 160 

Tides of rivers, bays, and lakes 162 

Atmospheric tide 166 

Planets. 

Origin of the name 167 

Planets long known 167 

Planets recently discovered 167 

Number of Planets and Asteroids . . . 168 
Distances — Dimensions of the system 169 
Mean distances, how determined by 

Kepler's law 170 

Magnitudes — diameters in miles 170 

Periodic times 171 

Inferior Planets, Mercury and Ye- 

nus 172 

Motions illustrated by Fig. 40 173 

Inferior and superior conjunction . . . 173 

Synodical revolution 173 

Direct and retrograde motions 174 

When the inferior planets are station- 
ary 175 

Phases of Mercury- and Yenus 176 

Eccentricity and inclination of their 

orbits 177 

When brightest 177 

Revolutions on their axes 178 



\ PAGE 

! Yenus as the evening and morning 

I star 178 

Position every eight years 178 

Transits of the inferior planets 179 

Transits of Mercury ISO 

Transits of Yenus 181 

Sun's Hor. Parallax by Transits of 

Yenus 1S2 

Superior Planets 183 

Mars — distance, color 1S3 

Changes in apparent size 184 

Phases, revolution on his axis 185 

I Jupiter — size, telescopic appearance.. 186 

Belts, satellites 1S7 

| Eclipses of the satellites. Fig. 44 139 

j Longitude by these eclipses 191 

Discovery of the progressive motion 

of light 193 

Saturn, telescopic appearance 194 

Dimensions of his system 194 

Saturn's Rings. Fig. 46 196 

Saturn's Satellites, number and ap- 
pearances 200 

Uranus — size, distance, discovery ... 201 

Satellites, number and motions 202 

Uniformity of direction in the plane- 
tary motions 202 

Neptune — size, distance, periodic time 203 

History of its discovery 203 

Asteroids, history of their discovery 204 

Number and names 206 

Distances, periodic times, size 206 

Motions of the Planetary System. 

Two methods of considering them . . . 208 

Conception of absolute space 20S 

Motions of the planets as seen from 

the sun 209 

Illustrated by the motions of Mercury 210 
Inadequate representations by dia- 
grams and orreries 211 

Apparent motions of the planets 212 

Of the Inferior planets by Fig. 40. . . 213 

Of Superior planets by Fig. 47 213 

Masses of the Planets 216 

Comparative density 216 

Stability of the Solar System 217 

Causes of disturbance 217 

How the perturbations were discov- 
ered 218 

Extreme minuteness of some of them 219 
Provisions for the stability of the sys- 
tem 220 

Numerical arrangement of the planets 221 

Comets and Meteoric Showers, 

Comet described, Fig. 43 221 

Number — Six most remarkable 223 

Magnitude and brightness 224 

Periods, distances, light 225 

Mass, proofs of its smallness 227 

Orbits and Motions 229 

Elements 230 



Vlll 



ANALYSIS. 



PARK 

How the return is predicted 23.2 

Halley's Comet 232 

Encke's Comet 233 

Proofs of a resisting medium 234 

Comet of 1843 235 

Physical nature of comets 236 

Dangers from them 237 

Meteoric Showers 238 

Meteoric shower of Nov. 18, 1833. ... 238 
Conclusions respecting them 240 

The Constellations. 

Fixed Stars— Classes 242 

Constellations 244 

Catalogues of the Stars 244 

Aries, "Taurus 246 

Gemini 247 

Cancer, Leo 24S 

Virgo, Libra, Scorpio 249 

Sagittarius, Capricornus, Aquarius . . 250 

Pisces, Little Bear 251 

Great Bear 252 

Draco 253 

Cepheus, Cassiopeia 254 

Camelopard, Andromeda, Perseus, 

Auriga 255 

Leo Minor, Grey Hounds, Berenice . 255 

Bootes, Crown, Hercules 256 

Lyre, Swan 257 

Little Fox, Eagle, Antinous 258 

Dolphin, Pegasus, Ophiuchus 258 



PAGE 

Whale, Orion, Hare, Canis Major and 

Minor 260 

Monoceros, Hydra 261 

Lesson for September 261 

Lesson for December 2G2 

Lesson for March 263 

Lesson for June 264 



Double, Temporary, and Variable 
Stars, and Nebulae. 

Great Telescopes , 265 

Double Stars, Number 267 

Multiple Stars 268 

Temporary Stars, Variable Stars . . . 269 

Clusters 270 

Nebulas, 271 

Nebula of Hercules 272 

Nebulous Stars 274 

Planetary Nebulae 275 

Galaxy 275 

Motions of the Stars 276 

Binary Stars ' 277 

Proper motions of the stars 278 

Motion of the Solar System 278 

Distances of the Stars 281 

Distance of 61 Cygni 2S2 

Amount of its parallax 282 

Nature of the Stars 284- 

System of the World 285 

Copernican System 286 



COMPENDIUM OF ASTRONOMY. 



PRELIMINARY OBSERVATIONS. 

1. Astronomy is that science which treats of the heav- 
enly bodies. 

More particularly, its object is to teach what is known 
respecting the Sun, Moon, Planets, Comets, and Fixed 
Stars ; and also to explain the methods by which this 
knowledge is acquired. 

Astronomy is sometimes divided into Descriptive, 
Physical, and Practical. Descriptive Astronomy re- 
spects facts ; Physical Astronomy, causes; Practical As- 
tronomy, the means of investigating the facts, whether 
by instruments, or by calculation. It is the province of 
Descriptive Astronomy to observe, classify, and record, 
all the phenomena of the heavenly bodies, whether per- 
taining to those bodies individually, or resulting from 
their motions and mutual relations. It is the part of 
Physical Astronomy to explain the causes of these phe- 
nomena by investigating and applying the general laws 
on which they depend ; especially by tracing out all the 
consequences of the law of universal gravitation. Prac- 
tical Astronomy lends its aid to both the other depart- 
ments. 

2. Astronomy is the most ancient of all the sciences. 
At a period of very high antiquity, it was cultivated in 
Egypt, in Chaldea, and in India. Such knowledge of 
the heavenly bodies as could be acquired by close and 
long continued observation, without the aid of instru- 



1 , Define Astronomy. What does it teach 1 Name the three 
parts into which it is divided. What does Descriptive Astron- 
omy respect ? What does Physical Astronomy ? What does 
Practical Astronomy ? What is the peculiar province of each ? 

1 



2 PRELIMINARY OBSERVATIONS. 

merits, was diligently amassed ; and tables of the celes- 
tial motions were constructed, which could be used in 
predicting eclipses, and other astronomical phenomena. 

About 500 years before the Christain era, Pythago- 
ras, of Greece, taught astronomy at the celebrated school 
at Crotona, (a Greek town on the southeastern coast of 
Italy.) and exhibited more correct views of the nature 
of the celestial motions, than were entertained by any 
other astronomer of the ancient world. His views, how- 
ever, were not generally adopted, but lay neglected for 
nearly 2000 years, when they were revived and estab- 
lished by Copernicus and Galileo. The most celebrated 
astronomical school of antiquity, was at Alexandria in 
Egypt, which was established and sustained by the Ptol- 
emies, (Egyptian princes,) 300 years before the Chris- 
tian era. The employment of instruments for measur- 
ing angles, and bringing in trigonometrical calculations 
to aid the naked powers of observation, gave to the Alex- 
andrian astronomers great advantages over all their pre- 
decessors. 

The most able astronomer of the Alexandrian school 
was Hipparchus, who was distinguished above all the 
ancients for the accuracy of his astronomical measure- 
ments and determinations. The knowledge of astron- 
omy possessed by the Alexandrian school, and recorded 
in the Almagest, or great work of Ptolemy, constituted 
the chief of what was known of our science during the 
middle ages, until the fifteenth and sixteenth centuries, 
when the labors of Copernicus of Prussia, Tycho Brake 



2. Trace the history of Astronomy. Among what ancient 
nations was it cultivated ? What kind of knowledge of the 
heavenly bodies was amassed ? Who was Pythagoras? When 
and where did he live ? Where was his school ? How correct 
were his views 1 Were they generally adopted ? Give an ac- 
count of the Alexandrian school. When was it established and 
by whom ? What gave it great advantages over all its prede- 
cessors ? Give some account of Hipparchus — of Ptolemy — of 
Copernicus — of Tycho Brahe — of Kepler — of Galileo — o! 
Newton — of La Place. Specify the respective labors of each. 



PRELIMINARY OBSERVATIONS 3 

of Denmark, Kepler of Germany, and Galileo of Italy, 
laid the solid foundations of modern astronomy. Coper- 
nicus expounded the true system of the world, or the 
arrangement and motions of the heavenly bodies ; Ty- 
cho Brahe carried the use of instruments, and the art of 
astronomical observation, to a far higher degree of accu- 
racy than had ever been done before ; Kepler discovered 
the v great laws which regulate the movements of the 
planets ; and Galileo, having first enjoyed the aid of the 
telescope, made innumerable discoveries in the solar 
system. Near the beginning of the eighteenth century, 
Sir Isaac Newton discovered, in the law of universal 
gravitation, tbo great principle mat explains the causes 
of all celestial phenomena ; and recently, La Place has 
more fully completed what Newton begun, having fol- 
lowed out all the consequences of the law of universal 
gravitation, in his great work, the Mecanique Celeste. 

3. Among the ancients, astronomy was studied chiefly 
as subsidiary to astrology. Astrology was the art of dv 
vining future events by the stars. It was of two kinds, 
natural and judicial. Natural Astrology, aimed at pre- 
dicting remarkable occurrences in the natural world, as 
eathquakes, volcanoes, tempests, and pestilential dis- 
eases. Judicial Astrology, aimed at foretelling the fates 
of individuals, or of empires. 

4. Astronomers of every age, have been distinguished 
for their persevering industry, and their great love of ac- 
curacy. They have uniformly aspired to an exactness 
in their inquiries, far beyond what is aimed at in most 
geographical investigations, satisfied with nothing short 
of numerical accuracy wherever this is attainable ; and 
years of toilsome observation, or laborious calculation, 
have been spent with the hope of attaining a few se- 



3. Define Astrology. What was Natural and what Judicial 
Astrology ? 

4. What is said of the industry and accuracy of astrono- 
mers 1 Can this science be taught by artificial aids alone ? 



PRELIMINARY OBSERVATIONS. 



conds nearer to the truth. Moreover, a severe but de- 
lightful labor is imposed on all, who would arrive at a 
clear and satisfactory knowledge of the subject of astron- 
omy. Diagrams, artificial globes, orreries, and familiar 
comparisons and illustrations, proposed by the author or 
the instructor, may afford essential aid to the learner, 
but nothing can convey to him a perfect comprehension 
of the celestial motions, without much diligent study 
and reflection. 

5. In this treatise, we shall for the present assume the 
Copernican system as the true system of the world, 
postponing the discussion of the evidence on which it 
rests to a late period, when the learner has been made ex- 
tensively acquainted with astronomical facts. This sys- 
tem maintains (1,) That the apparent diurnal revolution 
of the heavenly bodies, from east to west, is owing to 
the real revolution of the earth on its own axis from 
west to east, in the same time ; and (2,) That the sun 
is the center around which the earth and planets all re- 
volve from west to east, contrary to the opinion that the 
earth is the center of motion of the sun and planets. 



5. What system is assumed as the true system of the world ? 
Specify the two leading points in the Copernican system. 



PART I. OF THE EARTH, 



CHAPTER I. 



OF THE FIGURE AND DIMENSIONS OF THE EARTH, AND THE 
DOCTRINE OF THE SPHERE. 

6. The figure of the earth is nearly globular. This 
fact is known, lirst, by the circular form of its shadow 
cast upon the moon in a lunar eclipse ; secondly, from 
analogy, each of the other planets being seen to be 
spherical ; thirdly, by our seeing the tops of distant ob- 
jects while the other parts are invisible, as the topmast 
of a ship, while either leaving or approaching the shore, 
or the lantern of a light-house, which when first descried 
at a distance at sea, appears to glimmer upon the very 
surface of the water ; fourthly, by the testimony of nav- 
igators who have sailed around it ; and, finally, by ac- 
tual observations and measurements, made for the ex- 
press purpose of ascertaining the figure of the earth, b\ 
means of which astronomers are enabled to compute the 
distances from the center of the earth of various places 
on its surface, which distances are found to be nearly 
equal. 

The effect of the rotundity of the earth upon the ap- 
pearance of a ship, when either leaving or approaching 
the spectator, is illustrated by Fig. 1. 

As light proceeds in straight lines, it is evident that, 
if the earth is round, the top of the ship ought to come 
into view before the lower parts, when the ship is ap- 
proaching the spectator at A, and to remain longest in 
view when the ship is leaving him. But, were the earth 



6. What is the figure of the earth 1 Enumerate the various 
proofs of its rotundity. 

1* 




a continued plane, then the spectator would see all parts 
of the ship at the same time, as is represented in the an- 



nexed figure. 



Fig. 2. 




7. The foregoing considerations show that the form 
of the earth is spherical ; but more exact determinations 
prove, that the earth, though nearly globular, is not ex- 
actly so ; its diameter from the north to the south pole 
is about 26 miles less than through the equator, giving 
to the earth the form of an oblate spheroid, or a flattened 
sphere resembling an orange. We shall reserve the ex- 



FIGURE AND DIMENSIONS. 7 

planations of the methods by which this fact is estab- 
lished, until the learner is better prepared than at present 
to understand them. 

The mean or average diameter of the earth, is 7912.4 
miles, a measure which the learner should fix in his 
memory as a standard of comparison in astronomy, and 
of which he should endeavor to form the most adequate 
conception in his power. The circumference of the 
earth is about 25,000 miles. Although the surface of 
the earth is uneven, sometimes rising in high mountains, 
and sometimes descending in deep valleys, yet these ele- 
vations and depressions are so small in comparison with 
the immense volume of the globe, as hardly to occasion 
any sensible deviation from a surface uniformly curvi- 
linear. The irregularities of the earth's surface, in this 
view, are no greater than the rough points on the rind 
of an orange, which do not perceptibly interrupt its con 
tinuity ; for the highest mountain on the globe is only 
about five miles above the general level ; and the deep- 
est mine hitherto opened is only about half a mile.* 

5 i 

Now = , or about one sixteen hundredth part 

7912 1582 F 

of the whole diameter, an inequality which, in an arti- 
ficial globe of eighteen inches diameter, amounts to only 
the eighty eighth part of an inch. 

8. The greatest difficulty in the way of acquiring 
correct views in astronomy, arises from the erroneous 
notions trial pre-occupy the mind. To divest himself 



7. What is the exact figure of the earth 1 Flow much greater 
is its diameter through the equator than through the poles ? 
What is the mean average diameter of the earth ? What is its 
circumference ? Do the inequalities on the earth's surface af- 
fect its rotundity ? To what may these be compared ? How- 
high is the highest mountain above the general level 1 How 
deep is the deepest mine ? To how much would this amount 
on an artificial globe eighteen inches in diameter ? 

* Sir John Herschel. 



8 



THE EARTH. 



of these, the learner should conceive of the earth as a 
huge globe occupying a small portion of space, and en- 
circled on all sides with the starry sphere. He should 
free his mind from its habitual proneness to consider one 
part of space as naturally up and another down, and 
view himself as subject to a force which binds him to 
the earth as truly as though he were fastened to it by 
some invisible cords or wires, as the needle attaches it- 
self to all sides of a spherical loadstone. He should 

Fig. 3. 




dwell on this point until it appears to him as truly up in 
the direction of BB, CC, DD, (Fig. 3,) when he is at 
B, C, and D, respectively, as in the direction AA, when 
he is at A. 



DOCTRINE OF THE SPHERE. 



9. The definitions of the different lines, points, and 
circles, which are used in astronomy, and the proposi- 
tions founded upon them, compose the Doctrine of the 
Sphere. 



8. Whence arises the greatest difficulty in acquiring correct 
views in astronomy ? How should the learner conceive of 
the earth? Illustrate by figure 3. 

9. Doctrine of the sphere — define it. 



DOCTRINE OF THE SPHERE. 



10. A section of a sphere by a plane cutting it in any 
manner, is a circle. Great circles are those which pass 
through the center of the sphere, and divide it into two 
equal hemispheres : Small circles, are such as do not 
pass through the center, but divide the sphere into two 
unequal parts. Every circle, whether great or small, is 
divided into 360 equal parts called degrees. A degree, 
therefore, is not any fixed or definite quantity, but only 
a certain aliquot part of any circle.* 

The axis of a circle, is a straight line passing through 
its center at right angles to its plane. 



* As this work may be read by some who are unacquainted with 
even the rudiments of geometry, we annex a few particulars respecting 
angular measurements. 

A line drawn from the center to the circumference of a circle is 
called a radius, as CD, fig. 4. 

Any part of the circumference of a circle is called an arc, as AB, 
orBD. 



Fig. 4. 



An angle is measured by the 
arc included between two radii. 
Thus, in the annexed figure, the 
angle contained between the two 
radii CA and CB, that is, the an- 
gle ACB, is measured by the arc 
AB. But this arc is the same part 
of the smaller circle that EF is of 
the greater. The arc AB there- 
fore contains the same number of 
degrees as the arc EF, and either 
may be taken for the measure of 
the angle ACB. As the whole 
circle contains 360°, it is evident 
that the quarter of a circle, or quad- 
rant ABD, contains 90°, and the 
semicircle ABDG contains 180°. 

The complement of an arc or an- 
gle, is what it wants of 90°. Thus BD is the complement of AB, and 
AB is the complement of BD. If AB denotes a certain number of de- 
grees of latitude, BD will be the complement of the latitude or the co- 
latitude, as it is commonly written. 

The supplement of an arc or angle, is what it wants of IHtP. 
Thus BA is the supplement of GDB, and GDB, is the supplement 
of BA. If BA were 20° of longitude, GDB its supplement would 
be 160°. 

An angle is said to be subtended by the side which is opposite to it. 
Thus in the triangle ACK, the angle at C is subtended by the side AK, 
the angle at A by CK, and the angle at K by CA. In like manner a 
side is said to be subtended by an angle, as AK by the angle at C. 




10 the Earth. 

The pole of a great circle, is the point on the sphere 
where its axis cuts through the sphere. Every great 
circle has two poles, each of which is every where 90° 
from the great circle. 

All great circles of the sphere cut each other in two 
points diametrically opposite, and consequently, their 
points of section are 180° apart. 

A great circle which passes through the pole of an- 
other great circle, cuts the latter at right angles. 

The great circle which passes through the pole of an- 
other great circle and is at right angles to it, is called a 
secondary to that circle. 

The angle made by two great circles on the surface 
of the sphere, is measured by the arc of another great 
circle, of which the angular point is the pole, being the 
arc of that great circle intercepted between those two 
circles. 

11. In order to fix the position of any plane, either on 
the surface of the earth or in the heavens, both the earth 
and the heavens are conceived to be divided into sepa- 
rate portions by circles, which are imagined to cut 
through them in various ways. The earth thus inter- 
sected is called the terrestrial, and the heavens the ce- 
lestial sphere. The learner will remark, that these cir- 
cles have no existence in nature, but are mere land- 
marks, artificially contrived for convenience of refer- 



10. What figure is produced by the section of a sphere? 
Define great circles. Define small circles. Into how many 
degrees is every circle divided ? Is a degree any fixed or defi- 
nite quantity ? What is the axis of a circle ? What is the pole 
of a circle ? How do all great circles cut each other? How 
is a great circle cut by another great circle passing through its 
pole ? What is the secondary of a circle ? How is the angle 
madeby two great circles on the surface of the sphere measured? 

11. How are the earth and the heavens conceived to be di- 
vided ? What constitutes the terrestrial sphere ? What the 
celestial ? Have these circles any existence in nature ? In 
what do the heavenly bodies appear to be fixed ? 



OiiCTRlNh OF THE SPHERE. 11 

ence. On account of the immense distance of the heav- 
enly bodies, they appear to us, wherever we are placed. 
to be fixed in the same concave surface, or celestial 
vault. The great circles of- the globe, extended every 
way to meet the concave surface of the heavens, become 
circles of the celestial sphere. 

12. The Horizon is the great circle which divides 
the earth into upper and lower hemispheres, and sepa- 
rates the visible heavens from the invisible. This is 
the rational horizon. The sensible horizon, is a circle 
touching the earth at the place of the spectator, and is 
bounded by the line in which the earth and skies seem 
to meet. The sensible horizon is parallel to the ra- 
tional, but is distant from it by the semi-diameter of the 
earth, or nearly 4,000 miles. Still, so vast is the dis- 
tance of the starry sphere, that both these planes appear 
to cut that sphere in the same line ; so that we see the 
same hemisphere of stars that we should see if the up- 
per half of the earth were removed, and we stood on the 
rational horizon. 

13. The poles of the horizon are the zenith and na- 
dir. The Zenith is the point directly over our head, 
and the Nadir that directly under our feet. The plumb 
line is in the axis of the horizon, and consequently di- 
rected towards its poles. 

Every place on the surface of the earth has its own 
horizon; and the traveller has a new horizon at every 
step, always extending 00 degrees from him in all di- 
rections. 



12. Define the horizon. Distinguish between the rational 
and the sensible horizon. What is the distance between the 
sensible and rational horizons ? How do both appear to cut 
the starry heavens ? 

13. What are the poles of the horizon ? Define the zenith. 
Define the nadir. How is the plumb line situated with respect 
to the horizon? How manv horizons are there on the earth ? 



12 THE EARTH. 

14. Vertical circles are those which pass through the 
poles of the horizon, perpendicular to it. 

The Meridian is that vertical circle which passes 
through the north and south points. 

The Prime Vertical, is that vertica. circle which 
passes through the east and west points. 

The Altitude of a body, is its elevation above the ho- 
rizon, measured on a vertical circle. 

The Azimuth of a body, is its distance measured on 
the horizon from the meridian to a vertical circle passing 
through the body. 

The Amplitude of a body, is its distance on the hori- 
zon, from the prime vertical, to a vertical circle passing 
through the body. 

Azimuth is reckoned 90° from either the north or 
south point ; and amplitude 90° from either the east or 
west point. Azimuth and amplitude are mutually com- 
plements of each other. When a point is on the hori- 
zon, it is only necessary to count the number of degrees 
of the horizon between that point and the meridian, in 
order to find its azimuth ; but if the point is above the 
horizon, then its azimuth is estimated by passing a ver- 
tical circle through it, and reckoning the azimuth from 
the point where this circle cuts the horizon. 

The Zenith Distance of a body is measured on a ver- 
tical circle, passing through that body. It is the com- 
plement of the altitude. 

15. The Axis of the Earth is the diameter, on which 
the earth is conceived to turn in its diurnal revolution. 
The same line continued until it meets the starry con- 
cave, constitutes the axis of the celestial sphere. 



14. Define vertical circles — the meridian — the prime verti- 
cal — altitude — azimuth — amplitude. How many degrees of 
azimuth are reckoned ? from what points ? How are azimuth 
and amplitude related to each other ? Define zenith distance 
— How is it related to the altitude 1 

15. Define the axis of the earth — the axis of the celestial 
sphere — the poles of the earth — the poles of the heavens. 



DOCTRINE OF THE SPHERE. 13 

The Poles of the Earth are the extremities of the 
earth's axis : the Poles of the Heavens, the extremities 
of the celestial axis. 

16. The Equator is a great circle cutting the axis of 
the earth at right angles. Hence the axis of the earth 
is the axis of the equator, and its poles are the poles of 
the equator. The intersection of the plane of the equa- 
tor with the surface of the earth, constitutes the terres- 
trial, and with the concave sphere of the heavens, the 
celestial equator. The latter, by way of distinction, is 
sometimes denominated the equinoctial. 

17. The secondaries to the equator, that is, the great 
circles passing through the poles of the equator, are 
called Meridians, because that secondary which passes 
through the zenith of any place is the meridian of that 
place, and is at right angles both to the equator and the 
horizon, passing as it does through the poles of both. 
These secondaries are also called Hour Circles, because 
the arcs of the equator intercepted between them are 
used as measures of time. 

18. The Latitude of a place on the earth, is its dis- 
tance from the equator north or south. The Polar Dis- 
tance, or angular distance from the nearest pole, is the 
complement of the latitude. 

19. The Longitude of a place is its distance from 
some standard meridian, either east or west, measured 
on the equator. The meridian usually taken as the 
standard, is that of the Observatory of Greenwich, in 
London. If a place is directly on the equator, we have 
only to inquire how many degrees of the equator there 



16. Define the equator. What constitutes the terrestrial 
equator? what, the celestial equator ? What is this also called? 

17. What are the secondaries of the equator called 7 

18. Define the Latitude of a place- the polar distance. 

2 



14 THE EARTH. 

are between that place and the point where the meridian 
of Greenwich cuts the equator. If the place is north or 
south of the equator, then its longitude is the arc of the 
equator intercepted between the meridian which passes 
through the place, and the meridian of Greenwich. . 

20. The Ecliptic is a great circle in which the earth 
performs its annual revolution around the sun. It passes 
through the center of the earth and the center of the 
sun. It is found by observation that the earth does not 
lie with its axis at right angles to the plane of the eclip- 
tic, but that it is turned about 23^ degrees out of a per- 
pendicular direction, making an angle with the plane 
itself of 66^°. The equator, therefore, must be turned 
the same distance out of a coincidence with the ecliptic, 
the two circles making an angle with each other of 23 J°. 
It is particularly important for the learner to form cor- 
rect ideas of the ecliptic, and of its relations to the equa- 
tor, since to these two circles a great number of astro- 
nomical measurements and phenomena are referred. 

21. The Equinoctial Points, or Equinoxes* are the 
intersections of the ecliptic and equator. The time 
when the sun crosses the equator in going northward 
is called the vernal, and in returning southward, the au- 
tumnal equinox. The vernal equinox occurs about 
the 21st of March, and the autumnal the 22d of Sep- 
tember. 



19. Define the Longitude of a place. What is the standard 
meridian ? When a place is on the equator, how is its longi- 
tude measured 1 how when it is north or south of the equator ? 

20. Define the ecliptic. How does it pass with respect to 
the earth and the sun ? How is it situated with respect to the 
equator ? 

21. Define the equinoctial points. When is the vernal equi- 
nox, and when the autumnal ? 



* The term Equinoxes strictly denotes the times when the sun ar- 
rives at the equinoctial points, but it is frequently used to denote those 
points themselves. 



DOCTRINE OF THE SPHERE. 15 

22.. The Solstitial Points are the two points of the 
ecliptic most distant from the equator. The times when 
the sun comes to them are called solstices. The sum- 
mer solstice occurs about the 22d of June, and the win- 
ter solstice about the 22d of December. 

The ecliptic is divided into twelve equal parts of 30° 
each, called signs, which, beginning at the vernal equi- 
nox, succeed each other in the following order : 





Norther 7i. 




Southern. 




1. 


Aries 


cyo 


7. Libra 


.£. 


2. 


Taurus 


8 


8. Scorpio 


m 


3. 


Gemini 


H 


9. Sagittarius 


t 


4. 


Cancer 


<o> 


10. Capricornus 


vs 


5. 


Leo 


a 


11. Aquarius 


AAA/ 

AW 


6. 


Virgo 


m 


12. Pisces 


X 



The mode of reckoning on the ecliptic, is by signs, de- 
grees, minutes, and seconds. The sign is denoted either 
by its name or its number. Thus 100° maybe express- 
ed either as the 10th degree of Cancer, or as 3 s 10°. 

23. Of the various meridians, two are distinguished 
by the name of Colures. The Equinoctial Colure, is 
the meridian which passes through the equinoctial 
points. From this meridian, right ascension and celes- 
tial longitude are reckoned, as longitude on the earth is 
reckoned from the meridian of Greenwich. The Sol- 
stitial Colure, is the meridian which passes through the 
solstitial points. 

24. The position of a celestial body is referred to the 
equator by its right ascension and declination. Bight 



22. Define the solstitial points, and solstices. When does 
the summer solstice occur ? when does the winter solstice oc- 
cur ? Into how many signs is the ecliptic divided ? How 
many degrees are there in each ? Name the signs. What is 
the mode of reckoning on the ecliptic 1 In what two ways 
may 100° be expressed? 

23. What is the equinoctial colure ? — the solstitial colure 1 



16 THE EARTH. 

Ascension, is the angular distance from the vernal equi- 
nox measured on the equator. If a star is situated on 
the equator, then its right ascension is the number of 
degrees of the equator between the star and the vernal 
equinox. But if the star is north or south of the equa- 
tor, then its right ascension is the arc of the equator, in- 
tercepted between the vernal equinox and that secon- 
dary to the equator which passes through the star. De- 
clination is the distance of a body from the equator, 
measured on a secondary to the latter. Therefore, right 
ascension and declination correspond to terrestrial longi- 
tude and latitude, right ascension being reckoned from 
the equinoctial colure, in the same manner as longitude 
is reckoned from the meridian of Greenwich. On the 
other hand, celestial longitude and latitude are referred, 
not to the equator, but to the ecliptic. Celestial Longi- 
tude, is the distance of a body from the vernal equinox 
reckoned on the ecliptic. Celestial Latitude, is distance 
from the ecliptic measured on a secondary to the latter. 
Or, more briefly, Longitude is distance on the eclip- 
tic ; Latitude, distance from the ecliptic. The North 
Polar Distance of a star, is the complement of its de- 
clination. 

25. Parallels of Latitude are small circles parallel to 
the equator. They constantly diminish in size as we go 
from the equator to the pole. 

The Tropics are the parallels of latitude that pass 
through the solstices. The northern tropic is called the 
tropic of Cancer ; the southern, the tropic of Capricorn. 

The Polar Circles are the parallels of latitude that 
pass through the poles of the ecliptic, at the distance of 
23^ degrees from the pole of the earth. 



24. Define right ascension and declination. . To what do 
they correspond on the terrestrial sphere ? Define celestial 
longitude and latitude. 

25. What are parallels of latitude — tropics — polar circles 1 
To what is the elevation of the pole always equal ? also that 
of the equator ? 



DOCTRINE OF THE SPHERE. 17 

The elevation of the pole of the heavens above the 
horizon of any place, is always equal to the latitude of 
the place. Thus, in 40° of north latitude we see the 
north star 40° above the northern horizon, whereas, if 
we should travel southward its elevation would grow 
less and less, until we reached the equator, where it 
would appear in the horizon ; or, if we should travel 
northward, the north star would rise constantly higher 
and higher, until, if we could reach the pole of the earth, 
that star would appear directly over head. The eleva- 
tion of the equator above the horizon of any place, is 
equal to the complement of the latitude. Thus, at the 
latitude of 40° N. the equator is elevated 50° above the 
southern horizon. 

26. The earth is divided into five zones. That por- 
tion of the earth which lies between the tropics, is called 
the Torrid Zone ; that between the tropics and polar 
circles, the Temperate Zones; and that between the 
polar circles and the poles, the Frigid Zones. 

27. The Zodiac is the part of the celestial sphere, 
which lies about 8 degrees on each side of the ecliptic. 
This portion of the heavens is thus marked off by itself, 
because all the planets move within it. 

28. After endeavoring to form, from the definitions, 
as clear an idea as he can of the various circles of the 
sphere, the learner may next resort to an artificial globe, 
and see how they are severally represented there. Or if 
he has not access to a globe, he may aid his conceptions 
by the following easy device. To represent the earth, 
select a large apple, (a melon when in season will be 
found still better.) The shape of the apple, flattened as 



26. Define each of the zones. 

27. Define the zodiac. 

28. Show how to represent the artificial sphere by any round 
body as an apple, and point out the various circles on it. 

2* 



18 THE EARTH. 

it usually is at the two ends, will not inaptly exhibit 
the spheroidal figure of the earth, while the larger diam- 
eter through the middle will indicate the excess of mat- 
ter about the equator ; although we should remark, thai 
the disproportion between the polar and equatorial diam 
eters of the earth is in fact so slight, that it would be 
scarcely perceptible in a model. The eye and the stem 
of the apple will indicate the position of the two poles 
of the earth. Applying the thumb and finger of the 
left hand to the poles, and holding the apple so that the 
poles may be in a north and south line, turn the globe 
from west to east, and its motion will correspond to the 
diurnal movement of the globe. Pass a wire, as a knit- 
ting needle, through the poles, and it will represent the 
axis of the sphere. A circle cut around the apple half 
way between the poles, will be the equator; and several 
other circles cut between the equator and the poles, par- 
allel to the equator, will represent parallels of latitude, 
of which, two drawn 23 J degrees from the equator, will 
be the tropics, and two others at the same distance from 
the poles, will be the polar circles. A great circle cut 
through the poles in a north and south direction, will 
form the meridian, and several other great circles drawn 
through the poles, and of course perpendicularly to the 
equator, will be secondaries to the equator, constituting 
meridians or hour circles. A great circle cut through the 
center of the earth from one tropic to the other, will rep- 
resent the plane of the ecliptic, and consequently, a line 
cut around the apple where such a section meets the sur- 
face, is the terrestrial ecliptic. The points where this 
circle meets the tropics, are the solstices, and its intersec- 
tions with the equator are the equinoctial points. 

29. The horizon is best represented by a circular 
piece of pasteboard, cut so as to fit closely to the apple, 
being movable upon it. When this horizon is slipped 

29. How is the horizon represented in our model? How is 
it placed to represent the horizon of the equator 1 How for the 
horizon of the poles ? How for our own horizon 1 How shall 
we represent the prime vertical ? 



DOCTRINE OF THE SPHERE. ]p, 

up to the poles, it becomes the horizon of the equator ; 
when it is so placed as to coincide with the earth's 
equator, it becomes the horizon of the poles ; and in 
every other situation it represents the horizon of a place 
on the globe 90° every way from it. Suppose we are 
in latitude 40°, then let us place our movable paper par- 
allel to our own horizon, and elevate the pole 40° above 
it, as near as we can judge by the eye. If we cut a cir- 
cle around the apple, passing through its highest parts 
and through the east and west points, it will represent 
the prime vertical. 

30. We cannot too strongly recommend to the young 
learner to form for himself such a sphere as is here de- 
scribed, and to point out on it the various arcs of azimuth 
and altitude, right ascension and declination, terrestrial 
and celestial latitude and longitude, these last being re- 
ferred to the equator on the earth, and to the ecliptic in 
the heavens. 

31. When the circles of the sphere are well learned, 
we may advantageously employ projections of them in 
various illustrations. By the projection of the sphere is 
meant a representation of all its parts on a plane. The 
plane itself is called the plane of projection. Let us take 
any circular ring, as a wire bent into a circle, and hold 
it in different positions before the eye. If we hold it 
parallel to the face, or directly opposite to the eye, we 
see it as an entire circle. If we turn it a little sideways, 
it appears oval, or as an ellipse ; and as we continue to 
turn it more and more round, the ellipse grows narrower 
and narrower, until, when the edge is presented to the 
eye, we see nothing but a line. Now imagine the ring 
to be near a perpendicular wall, and the eye to be re- 



30. What is particularly recommended to the young learner? 

31 What is meant by the projection of the sphere ? What 
is the projection of a circle when seen directlybefore the face ? 
what when seen obliquely 1 what when seen edgewise ? 



20 



THE EARTH. 



moved at such a distance from it, as not to distinguish 
any interval between the ring and the wall ; then the 
several figures under which the ring is seen, will appear 
to be inscribed on the wall, and we shall see the ring as 
a circle when perpendicular to a straight line joining 
the center of the ring and the eye, as an ellipse when 
oblique to this line, or as a straight line when its edge is 
towards us. 

32. It is in this manner that the circles of the sphere 
are projected, as represented in the following diagram 




Here various circles are represented as projected on the 
meridian, which is supposed to be situated directly be- 
fore the eye, at some distance from it. The horizon HO 
being perpendicular to the meridian is seen edgewise, and 
consequently is projected into a straight line. The same 
is the case with the prime vertical ZN, with the equator 
EQ, and the several small circles parallel to the equator, 
which represent the two tropics and the two polar cir- 



32. In figure 5, what represents the plane of projection ? 
Why are certain circles represented by straight lines 1 why are 
others represented by ellipses ? How is the eye supposed to 
be situated ? 



DIURNAL REVOLUTION 21 

cles. In fact, all circles whatsoever, which are perpen- 
dicular to the plane of projection, will be represented 
by straight lines. But every circle which is perpendic- 
ular to the horizon, except the prime vertical, being seen 
obliquely as ZMN, will be projected into an ellipse. 
In the same manner, PRP, an hour circle, being oblique 
to the eye, is represented by an ellipse on the plane of 
projection. 



CHAPTER II. 

DIURNAL REVOLUTION ARTIFICIAL GLOBES. 

33. The apparent diurnal revolution of the heavenly 
bodies from east to west, is owing to the actual revolu- 
tion of the earth on its own axis from west to east. If 
we conceive of a radius of the earth's equator extended 
until it meets the concave sphere of the heavens, then 
as the earth revolves, the extremity of this line would 
trace out a curve on the face of the sky, namely, the ce- 
lestial equator. In curves parallel to this, called the cir- 
cles of diurnal revolution, the heavenly bodies actually 
appear to move, every star having its own peculiar cir- 
cle. After the learner has first rendered familiar the 
real motions of the earth from west to east, he may 
then, without danger of misconception, adopt the com- 
mon language, that all the heavenly bodies revolve 
around the earth once a day from east to west, in circles 
parallel to the equator and to each other. 

34. The time occupied by a star in passing from any 
point in the meridian until it comes round to the same 



33. To what is the apparent diurnal revolution of the heav- 
enly bodies from east to west owing ? If a radius of the earth's 
equator were extended to meet the concave sphere of the heav- 
ens, what would it trace out as the earth revolves ? What 
are circles of diurnal revolution 1 



22 THE EARTH. 

point again, is called a sidereal day, and measures the 
period of the earth's revolution on its axis. If we watch 
the returns of the same star from day to day, we shall 
find the intervals exactly equal to one another ; that is< 
the sidereal days are all equal. Whatever star we se- 
lect for the observation, the same result will be obtained. 
The stars, therefore, always keep the same relative posi- 
tion, and have a common movement round the earth — 
a consequence that naturally flows from the hypothesis, 
that their apparent motion is all produced by a single 
real motion, namely, that of the earth. The sun, moon, 
and planets, as well the fixed stars, revolve in like man- 
ner, but their returns to the meridian are not, like those 
of the fixed stars, at exactly equal intervals. 

35. The appearances of the diurnal motions of the 
heavenly bodies are different in different parts of the 
earth, since every place has its own horizon, (Art. 8,) 
and different horizons are variously inclined to each 
other. Let us suppose the spectator viewing the diurnal 
revolutions from several different positions on the earth. 

On the equator, his horizon would pass through both 
poles ; for the horizon cuts the celestial vault at 90 de- 
grees in every direction from the zenith of the spectator ; 
but the pole is likewise 90 degrees from his zenith, and 
consequently, the pole must be in the horizon. The ce- 
lestial equator would coincide with the Prime Vertical 



34. Define a sidereal day. Are the sidereal days equal oi 
unequal ? Are the returns of the sun, moon, and planets to 
the meridian, likewise at equal intervals ? 

35. How are the appearances of the diurnal motions in dif- 
ferent parts of the earth ? When the spectator is on the equa- 
tor, where would his horizon pass with respect to the poles of 
the earth? With what great circle would the celestial equator 
coincide ? How would all the circles of diurnal revolution be 
situated with respect to the horizon ? Define a right sphere. 
In a right sphere, how would a star situated in *he celestial 
equator perform its circuit? how would stars nearer the poles 
appear to move 1 



DIURNAL REVOLUTION. 23 

being a great circle passing through the east and west 
points. Since all the diurnal circles are parallel to the 
equator, consequently, they would all, like the equator, 
be perpendicular to the horizon. Such a view of the 
heavenly bodies, is called a right sphere ; or, 

A Right Sphere is one in which all the daily revolu- 
tions of the stars, are in circles perpendicular to the horizon. 

A right sphere is seen only at the equator. Any star 
situated in the celestial equator, would appear to rise di- 
rectly in the east, when on the meridian to be in the 
zenith of the spectator, and to set directly in the west ; 
in proportion as stars are at a greater distance from the 
equator towards the pole, s they describe smaller and 
smaller circles, until, near the pole, their motion is hardly 
perceptible. 

36. If the spectator advances one degree towards the 
north pole, his horizon reaches one degree beyond the 
pole of the earth, and cuts the starry sphere one degree 
below the pole of the heavens, or below the north star, 
if that be taken as the place of the pole. As he moves 
onward towards the pole, his horizon continually reaches 
farther and farther beyond it, until when he comes to 
the pole of the earth, and under the pole of the heavens, 
his horizon reaches on all sides to the equator and coin- 
cides with it. Moreover, since all the circles of daily 
motion are parallel to the equator, they become, to the 
spectator at the pole, parallel to the horizon. This is 
what constitutes a parallel sphere. Or, 

A Parallel Sphere is that in which all the circles of 
daily motion arc parallel to the horizon. 

To render this view of the heavens familiar, the 
learner should follow round in his mind a number of 



36. What changes take place in one's horizon as he moves 
from the equator towards the pole ? How would it be situated 
when he reached the pole 1 Define a parallel sphere. Explain 
the appearances of the stars and of the sun in a parallel sphere. 
Where only can such a sphere be seen ? Has the pole of the 
earth ever been reached by man 1 



24 THE EARTH. 

separate stars, one near the horizon, one a few degrees 
above it, and a third near the zenith. To one who 
stood upon the north pole, the stars of the northern hemi- 
sphere would all be perpetually in view when not ob- 
scured by clouds or lost in the sun's light, and none of 
those of the southern hemisphere would ever be seen. 
The sun would be constantly above the horizon for six 
months in the year, and the remaining six constantly 
out of sight. That is, at the pole the days and nights 
are each six months long. The phenomena at the south 
pole are similar to those at the north. 

A perfect parallel sphere can never be seen except at 
one of the poles — a point which has never been actually 
reached by man ; yet the British discovery ships pene- 
trated within a few degrees of the north pole, and of 
course enjoyed the view of a sphere nearly parallel. 

37. As the circles of daily motion are parallel to the 
horizon of the pole, and perpendicular to that of the 
equator, so at all places between the two, the diurnal 
motions are oblique to the horizon. This aspect of the 
heavens constitutes an oblique sphere, which is thus de- 
fined: 

An Oblique Sphere is that in which the circles of 
daily motion are oblique to the horizon. 

Suppose, for example, the spectator is at the latitude of 
fifty degrees. His horizon reaches 50° beyond the pole 
of the earth, and gives the same apparent elevation to 
the pole of the heavens. It cuts the equator, and all 
the circles of daily motion, at an angle of 40°, being al- 
ways equal to the co-altitude of the pole. Thus, let HO 
(Fig. 6,) represent the horizon, EQ, the equator, and 
PP' the axis of the earth. Also, 11, mm, &c, parallels 
of latitude. Then the horizon of a spectator at Z, in 
latitude 50° reaches to 50° beyond the pole ; and the 
angle ECH, is 40°. As we advance still farther north 



37. Define an oblique sphere. Where is it seen ? At the 
latitude of 50° how is the horizon situated ? Illustrate by fig. 6. 



25 







77^^? 


/& 


"*x 


' /' 


e/ 




7\ 


ID 


- ^^^ 


7^0 


l^"-\ 


\/ 


\ 7i \ 


W>s 







the elevation of the diurnal circles grows less and less, 
and consequently the motions of the heavenly bodies 
more and more oblique, until finally, at the pole, where 
the latitude is 90°, the angle of elevation of the equator 
vanishes, and the horizon and equator coincide with 
each other, as before stated. 

38. The circle of perpetual apparition, is the 

boundary of that space around the elevated pole, where 
the stars never set. Its distance from the pole is equal 
to the latitude of the place. For, since the altitude of 
the pole is equal to the latitude, a star whose polar dis- 
tance is just equal to the latitude, will when at its low- 
est point only just reach the horizon ; and all the stars 
nearer the pole than this will evidently not descend so 
far as the horizon. 

Thus, mm (Fig. 6,) is the circle of perpetual appari- 
tion, between which and the north pole, the stars never 
set, and its distance from the pole OP is evidently equal 
to the ehvation of the pole, and of course to the lati- 
tude. 



38. What is the circle of perpetual apparition? 
by fig. 6. 

3 



Illustrate 



26 THE EARTH 

39. In the opposite hemisphere, a similar part of the 
sphere adjacent to the depressed pole never rises. Hence 

The circle of perpetual occultation, is the boun- 
dary of that space around the depressed pole, within 
which the stars never rise. Thus, m'm (Fig. 6,) is the 
circle of perpetual occultation, between which and tho 
south pole, the stars never rise. 

40. In an oblique sphere, the horizon cuts the circles 
of daily motion unequally. Towards the elevated pole, 
more than half the circle is above the horizon, and a 
greater and greater portion as the distance from the 
equator is increased, until finally, within the circle of 
perpetual apparition, the whole circle is above the hori- 
zon. Just the opposite takes place in the hemisphere 
next the depressed pole. Accordingly, when the sun is 
in the equator, as the equator and horizon, like all other 
grsat circles of the sphere, bisect each other, the days 
and nights are equal all over the globe. But when the 
sun is north of the equator, the days become longer than 
the nights, but shorter when the sun is south of the 
equator. Moreover, the higher the latitude, the greater 
is the inequality in the lengths of the days and nights. 
All these ooints will be readily understood by inspecting 
figure 

41. Most of the appearances of the diurnal t evolution 
can be explained, either on the supposition that the ce- 
lestial sphere actually all turns around the earth once in 
24 hours, or that this motion of the heavens is merely 
apparent, arising from the revolution of the earth on its 



39. What is the circle of perpetual occultation ? Illustrate 
by fig. 6. 

40. How does the horizon of an oblique sphere cut the cir- 
cles of daily motion ? Towards the elevated pole what portion 
of the circles is above the horizon? Towards the depressed 
pole, how is the fact? When are the days and nights equal 
all over the world ? When are the days longer, and whsii 
shorter than the nights ? 



DIURNAL REVOLUTION. 27 

axis in the opposite direction — a motion of which we 
are insensible, as we sometimes lose the consciousness 
of our own motion in a ship or a steamboat, and observe 
all external objects to be receding from us with a com- 
mon motion. Proofs entirely conclusive and satisfac- 
tory, establish the fact, that it is the earth and not the 
celestial sphere that turns ; but these proofs are drawn 
from various sources, and the student is not prepared to 
appreciate their value, or even to understand some of 
them, until he has made considerable proficiency in the 
study of astronomy, and become familiar with a great 
variety of astronomical phenomena. To such a period 
of our course of instruction, we therefore postpone the 
discussion of the hypothesis of the earth's rotation on 
its axis. 

42. While we retain the same place on the earth, the 
diurnal revolution occasions no change in our horizon, 
but our horizon goes round as well as ourselves. Let 
us first take our station on the equator at sunrise ; our 
horizon now passes through both the poles, and through 
the sun, which we are to conceive of as at a great dis- 
tance from the earth, and therefore as cut, not by the 
terrestrial but by the celestial horizon. As the earth 
turns, the horizon dips more and more below the sun, at 
the rate of 15 degrees for every hour, and, as in the case 
of the polar star, the sun appears to rise at the same rate. 
In six hours, therefore, it is depressed 90 degrees below 
the sun, which brings us directly under the sun, which, 
for our present purpose, we may consider as having all 
the while maintained the same fixed position in space. 



4 1 . On what suppositions can the appearances of the diurnal 
revolution be explained ? Is it the earth or the heavens that 
really move I Why is the discussion of this subject postponed ? 

42. Explain the true cause of the sun's appearing to rise and 
set, as observed at the equator. What is the position of the ho- 
rizon at sunrise ? What at. six hours afterwards 1 What at 
the end of twelve hours 1 What at the end of eighteen hours'' 



28 THE EARTH. 

The earth continues to turn, and in six hours more, it 
completely reverses the position of our horizon, so that 
the western part of the horizon which at sunrise was 
diametrically opposite to the sun now cuts the sun, and 
soon afterwards it rises above the level of the sun, and 
the sun sets. During the next twelve hours, the sun 
continues on the invisible side of the sphere, until the 
horizon returns to the position from which it started, and 
a new day begins. 

43. Let us next contemplate the similar phenomena 
at the poles. Here the horizon, coinciding as it does 
with the equator, would cut the sun through its center, 
and the sun would appear to revolve along the surface 
of the sea, one-half above and the other half below the 
horizon. This supposes the sun in its annual revolution 
to be at one of the equinoxes. When the sun is north 
of the equator, it revolves continually round in a circle, 
which, during a single revolution, appears parallel to the 
equator, and it is constantly day ; and when the sun 
is south of the equator, it is, for the same reason, contin- 
ual night. 

We have endeavored to conceive of the manner in 
which the apparent diurnal movements of the sun are 
really produced at two stations, namely, in the right 
sphere, and in the parallel sphere. These two cases 
being clearly understood, there will be little difficulty in 
applying a similar explanation to an oblique sphere. 



ARTIFICIAL GLOBES. 

44. Artificial globes are of two kinds, terrestrial and 
celestial. The first exhibits a miniature representation 
of the earth ; the second, of the visible heavens ; and 
both show the various circles by which the two spheres 



43. Explain the similar phenomena at the poles, first, when 
the sun is at the equinoxes, and secondly, when it is north and 
when it is south of the equator. 



ARTIFICIAL GLOBES. 29 

are respectively traversed Since all globes are similar 
solid figures, a small globe, imagined to be situated at 
the center of the earth or of the celestial vault, may rep- 
resent all the visible objects and artificial divisions of 
either sphere, and with great accuracy and just propor- 
tions, though on a scale greatly reduced. The study of 
artificial globes, therefore, cannot be too strongly recom- 
mended to the student of astronomy.* 

45. An artificial globe is encompassed from north to 
south by a strong brass ring to represent the meridian of 
the place. This ring is made fast to the two poles and 
thus supports the globe, while it is itself supported in a 
vertical position by means of a frame, the ring being 
usually let into a socket in which it may be easily slid, 
so as to give any required elevation to the pole. The 
brass meridian is graduated each way from the equator 
to the pole 90°, to measure degrees of latitude or decli- 
nation, according as the distance from the equator refers 
to a point on the earth or in the heavens. The horizon 
is represented by a broad zone, made broad for the con- 
venience of carrying on it a circle of azimuth, another of 
amplitude, and a wide space on w T hich are delineated 
the signs of the ecliptic, and the sun's place for every 
day in the year ; not because these points have any spe- 
cial connexion with the horizon, but because this broad 
surface furnishes a convenient place for recording them. 



44. What does the terrestrial globe exhibit ? What does 
the celestial globe ? What do both show ? 

45. How is the meridian of the place represented ? To what 
points is the brass meridian fastened ? What supports the ring ? 
How is it graduated ? How is the horizon represented ? Why 
is it made broad ? What circles are inscribed on it 1 



* It were .esirable, indeed, that every student of the science should 
have a celestial globe, at least, constantly before him. One of a 
small size, as eight or nine inches, will answer the purpose, although 
globes of these dimensions cannot usually be relied on for nice meas- 
urements 

3* 



30 THE EARTH. 

46. Hour Circles are represented on the terrestrial 
globe by great circles drawn through the pole of the 
equator ; but, on the celestial globe, corresponding cir- 
cles pass through the poles of the ecliptic, constituting 
circles of latitude, while the brass meridian, being a se- 
condary to the equinoctial, becomes an hour circle of 
any star which, by turning the globe, is brought under it. 

47. The Hour Index is a small circle described around 
the pole of the equator, on which are marked the hours 
of the day. As this circle turns along with the globe, it 
makes a complete revolution in the same time with the 
equator ; or, for any less period, the same number of de- 
grees of this circle and of the equator pass under the 
meridian. Hence the hour index measures arcs of right 
ascension, 15° passing under the meridian every hour. 

48. The Quadrant of Altitude is a flexible strip of 
brass, graduated into ninety equal parts, corresponding 
in length to degrees on the globe, so that when applied to 
the globe and bent so as closely to fit its surface, it meas- 
ures the angular distance between any two points. 
When the zero, or the point where the graduation be- 
gins, is laid on the pole of any great circle, the 90th de- 
gree will reach to the circumference of that circle, and 
being therefore a great circle passing through the pole 
of another great circle, it becomes a secondary to the 
latter. Thus the quadrant of altitude may be used as a 
secondary to any great circle on the sphere ; but it is 
used chiefly as a secondary to the horizon, the point 



46. How are hour circles represented on the terrestrial 
globe ? How are circles of latitude represented on the celes- 
tial globe ? 

47. Describe the hour index. What does it measure ? 

48. What is the quadrant of altitude? How is it gradua- 
ted ? When the zero point is laid on the pole of any great cir- 
cle, to what will the 90th degree reach ? How may it be used 
as a secondary to any great circle ? When screwed on the 
zenith what does it become ? What arcs does it then measure ? 



TERRESTRIAL GLOBE. 31 

marked 90° being screwed fast to the pole of the hori- 
zon, that is, the zenith, and the other end, marked 0. 
being slid along between the surface of the sphere and 
the wooden horizon. It thus becomes a vertical circle, 
on which to measure the altitude of any star through 
which it passes, or from which to measure the azimuth 
of the star, which is the arc of the horizon intercepted 
between the meridian and the quadrant of altitude pass- 
ing through the star. 

49. To rectify the. globe for any place, the north pole 
must be elevated to the latitude of the place ; then the 
equator and all the diurnal circles will have their due in- 
clination in respect to the horizon ; and, on turning the 
globe, every point on either globe will revolve as the 
same point does in nature ; and the relative situations of 
all places will be the same as on the native spheres. 

PROBLEMS ON THE TERRESTRIAL GLOBE. 

50. To find the Latitude and Longitude of a place : 
Turn the globe so as to bring the place to the brass me- 
ridian ; then the degree and minute on the meridian di- 
rectly over the place will indicate its latitude, and the 
point of the equator under the meridian, will show its 
longitude. 

Ex. What is the Latitude and Longitude of the city 
of New York? 

51. To find a place having its Latitude and Longitude 
given : Bring to the brass meridian the point of the equa- 
tor corresponding to the longitude, and then at the de- 
gree of the meridian denoting the latitude, the place will 
be found. 

Ex. What place on the globe is in Latitude 39° N. and 
Longitude 77° W. 1 



49. How do .ve rectify the globe for any place ? 

50. Find the latitude and longitude of Washington City. 

51. What place lies in latitude 39° N.and longitude 77° W.? 



32 THE EARTH 

52. To find the bearing and distance of two places : 
Rectify the globe for one of the places ; screw the quad- 
rant of altitude to the zenith,* and let it pass through 
the other place. Then the azimuth will give the bear- 
ing of the second place from the first, and the number 
of degrees on the quadrant of altitude, multiplied by G9, 
(the number of miles in a degree,) will give the distance 
between the two places. 

Ex. What is the bearing of New Orleans from New 
York, and what is the distance between these places 1 

53. To determine the difference of time in different 
places : Bring the place that lies eastward of the other 
to the meridian, and set the hour index at XII. Turn 
the globe eastward until the other place comes to the 
meridian, then the index will point to the hour required. 

Ex. When it is noon at New York, what time is it at 
London ? 

54. The hour being given at any place, to tell what 
hour it is in any other part of the world: Bring the 
given place to the meridian, and set the hour index to 
the given time ; then turn the globe, until the other 
place comes under the meridian, and the index will 
point to the required hour. 

Ex. What time is it at Canton, in China, when it is 
9 o'clock A. M. at New York ? 

55. To find what people on the earth live under us, 
having their noon at the time of our midnight : Bring 
the place where we dwell to the meridian, and set the 



52. What is the bearing and distance of New Orleans from 
New York ? 

53. When it is noon at New York, what time is it at Pekin ? 

54. What time is it at London when it is noon at Boston 1 



* The zenith will of course be the point of the meridian over the 
place. 



TERRESTRIAL GLOBE. 33 

hour index to XII ; then turn the globe until the other 
XII comes under the meridian; the point under the 
same part of the meridian where we were before, will 
be the place sought. 

Ex. Find what place is directly under New York. 

56. To find what people of the southern hemisphere 
are directly opposite to us : Bring our place to the me- 
ridian ; the place in the same latitude south, then un- 
der the meridian, will be the place in question. 

Ex. What place in the southern hemisphere corres- 
ponds to New Haven ? 

57. To find the antipodes of a place, or the people 
whose feet are exactly opposite to ours : Bring our place 
to the meridian ; set the hour index to XII, and turn the 
globe until the other XII comes under the meridian ; 
then the point of the southern hemisphere under the me- 
ridian and having the same latitude with ours, will be 
the place of our antipodes. 

Ex. Who are antipodes to the people of Philadelphia ? 

58. To rectify the globe for the sun's place: On the 
wooden horizon, find the day of the month, and against 
it is given the sun's place in the ecliptic, expressed by 
signs and degrees.* Look for the same sign and degree 
on the ecliptic, bring that point to the meridian and set 
the hour index to XII. To all places under the merid- 
ian it will then be noon. 

Ex. Rectify the globe for the sun's place on the 1st 
of September. 



55. Find what place is directly under Philadelphia. 

56. What place in south latitude corresponds to Boston 7 
51. Who are the antipodes of the people of London ? 

58. Rectify the globe for the sun's place for the first of June. 



* The larger globes have the day of the month marked against *he 
corresponding sign on the ecliptic itself. 



34 THE EARTH. 

59. Trie latitude of the place being given, to find the 
time of the sun's rising and setting on any given day 
at that place: Having rectified the globe for the lati- 
tude, bring the sun's place in the ecliptic to the gradua- 
ted edge of the meridian, and set the hoar index to XII ; 
then turn the globe so as to bring the sun to the eastern 
and then to the western horizon, and the hour index 
will show the times of rising and setting respectively. 

Ex. At what time will the sun rise and set at New 
Haven, Lat. 41° 18', on the 10th of July ? 

PROBLEMS ON THE CELESTIAL GLOBE. 

60. To find the Declination and Right Ascension of 
a heavenly body : Bring the place of the body (whether 
sun or star) to the meridian. Then the degree and 
minute standing over it will show its declination, and 
the point of the equinoctial under the meridian will give 
its right ascension. It will be remarked, that the decli- 
nation and right ascension are found in the same man- 
ner as latitude and longitude on the terrestrial globe. 
Right ascension is expressed either in degrees or in 
hours ; both being reckoned from the vernal equinox. 

Ex. What is the declination and right ascension of the 
bright star Lyra? — also of the sun on the 5th of June? 



61. To represent the appearance of the heavens at any 
time : Rectify the globe for the latitude, bring the sun's 
place in the ecliptic to the meridian, and set the hour 
index to XII ; then turn the globe westward until the 
index points to the given hour, and the constellations 
would then have the same appearance to an eye situated 



59. Find the time of the sun's rising and setting at Boston 
(Lat. 42°, Lon. 71°) on the first day of December. 

60. On the celestial globe, What is the right ascension and 
declination of any star taken at pleasure ? 

61. Represent the appearance of the heavens at Tuscaloosa 
(Lat. 33°, Lon. 87°) at 8 o'clock in the evening of Nov. 13th. 



CELESTIAL GLOBE. 35 

at the center of the globe, as they have at that moment 
in the sky. 

Ex. Required the aspect of the stars at New Haven, 
Lat. 41° 18', at 10 o'clock, on the evening of Decem- 
ber 5th. 

62. To find the altitude and azimuth of any star . 
Rectify the globe for the latitude, and let the quadrant 
of altitude be screwed to the zenith, and be made to pass 
through the star. The arc on the quadrant, from the 
horizon to the star, will denote its altitude, and the arc 
of the horizon from the meridian to the quadrant, will be 
its azimuth. 

Ex. What is the altitude and azimuth of Sirius (the 
brightest of the fixed stars) on the 25th of December at 
10 o'clock in the evening, in Lat. 41° 1 

63. To find the angular distance of two stars from 
each other : Apply the zero mark of the quadrant of alti- 
tude to one of the stars, and the point of the quadrant 
which falls on the other star, will show the angular dis- 
tance between the two. 

Ex. What is the distance between the two largest 
stars of the Great Bear.* 

64. To find the sun's meridian altitude, the latitude 
ind day of the month being given : Having rectified 
the globe for the latitude, bring the sun's place in the 
ecliptic to the meridian, and count the number of de- 



62. Find the altitude and azimuth of Lyra at 10 o'clock in 
the evening of June 18th, in Lat. 42°. 

63. Find the angular distance between any two stars taken 
at pleasure. 



* These two stars are sometimes called "the Pointers," from the line 
which passes through them being always nearly in the direction of the 
north star. The angular distance between them is about 5°, and may 
be learned as a standard of reference in estimating by the eye, the dis- 
tance between any two points on the celestial vault. 



36 



THE EARTH, 



grees and minutes between that point of the meridian 
and the zenith. The complement of this arc will be 
the sun's meridian altitude. 

Ex. What is the sun's meridian altitude at noon on 
the 1st of August, in Lat. 41° 18'? 



CHAPTER III. 

OF PARALLAX, REFRACTION, AND TWILIGHT. 

65. Parallax is the apparent change of place which 
bodies undergo by being viewed from different points. 



Fig- 7 




Thus in figure 7, let A represent the earth, CH the ho- 
rizon. HZ a quadrant of a great circle of the heavens, 



64. What is the sun's meridian altitude at noon on the 18th 
of June, in latitude 35° ? 

65. Define parallax. Illustrate by the figure. What angle 
measures the parallax? Why do astronomers consider the 
heavenly bodies as viewed from the center of the earth ? 



PARALLAX. 3? 

extending from the horizon to the zenith ; and let E, F, 
G, O, be successive positions of the moon at different 
elevations, from the horizon to the meridian. Now a 
spectator on the surface of the earth at A, would refer 
the place of E to h, whereas, if seen from the center of 
the earth, it w T ould appear at H. The arc Hh is called 
the parallactic arc, and the angle HEA, or its equal AEC, 
is the angle of parallax. The same is true of the angles 
at F, G, and O, respectively. 

Since then a heavenly body is liable to be referred to 
different points on the celestial vault, when seen from 
different parts of the earth, and thus some confusion 
occasioned in the determination of points on the celes- 
tial sphere, astronomers have agreed to consider the true 
place of a celestial object to be that, where it would 
appear if seen from the center of the earth. The doc- 
trine of parallax teaches how to reduce observations 
made at any place on the surface of the earth, to such as 
hey would be if made from the center. 

66. The angle AEC is called the horizonta parallax, 
which may be thus defined. Horizontal Parallax, is 
the change of position which a celestial body, appearing 
in the horizon as seen from the surface of the earth, 
would assume if viewed from the earth's center. It is 
the angle subtended by the semi-diameter of the earth, 
as viewed from the body itself. 

It is evident from the figure, that the effect of parallax 
upon the place of a celestial body is to depress it. Thus, 
in consequence of parallax, E is depressed by the arc 
Hh ; F by the arc Vp ; G by the arc Rr ; while O sus- 
tains no change. Hence, in all observations on the al- 
titude of the sun, moon, or planets, the amount of par- 
allax is to be added : the stars, as we shall see here- 
after, have no sensible parallax. 



66. Define horizontal parallax — By what is it subtended? 
(See Art. 10. Note.) What is the effect of parallax upon the 
place of a heavenly body? 

4 



38 



THE EARTH. 



67. The determination of the horizontal parallax of a 
celestial body is an element of great importance, since it 
furnishes the means of estimating the distance of the 
body from the center of the earth. Thus, if the angle 
AEC (Fig 7,) be found, the radius of the earth AC be- 
ing known, we have in the right angled triangle AEC, 
the side AC and all the angles, to find the side CE, 
which is the distance of the moon from the center of 
the earth.* 

REFRACTION. 

68. While parallax depresses the celestial bodies sub- 
ject to it, refraction elevates them ; and it affects alike 
(he most distant as well as nearer bodies, being occa- 
sioned by the change of direction which light undergoes 

Fig. 8. 




67. Why is the determination of the parallax of a heavenly 
body an element of great importance ? Illustrate by figure 7. 



* Should the reader be unacquainted with the principles of trigonom- 
etry, yet he ought to know the fact that these principles enable us, 
when we have ascertained certain parts in a triangle, to find the un- 
known parts. Thus, in the above case, when w T e have found the an- 
gle of parallax, AEB, (which is determined by certain astronomical ob- 
servations,) knowing also the semi-diameter of the earth AC, we can 
find by trigonometry, the length of the side CE, which is the distance 
of the body from the center of the earth. 



REFRACTION. 39 

m passing through the atmosphere. Let us conceive of 
the atmosphere as made up of a great number of concen- 
tric strata, as AA, BB, CC, and DD, (Fig. 8,) increasing 
rapidly in density (as is known to be the fact) in ap- 
proaching near to the surface of the earth. Let S be a 
star, from which a ray of light S« enters the atmosphere 
at «, where, being much turned towards the radius of 
the convex surface,* it would change its direction into 
the line ab, and again into be, and cO, reaching the 
eye at O. Now, since an object always appears in the 
direction in which the light finally strikes the eye, the 
star would be seen in the direction of the ray Oc, and 
therefore, the star would apparently change its place, 
in consequence of refraction, from S to S', being ele- 
vated out of its true position. Moreover, since on ac- 
count of the continual increase of density in descending 
through the atmosphere, the light would be continually 
turned out of its course more and more, it would there- 
fore move, not in the polygon represented in the figure, 
but in a corresponding curve, whose curvature is rapidly 
increased near the surface of the earth. 



68. What effect has refraction upon the place of a heavenly 
body? By whatis it occasioned ? Illustrate by figure 8. How- 
is a ray of light affected by passing out of a rarer into a denser 
medium? Why is an oar bent in the water ? In what line 
does the light move as it goes through the atmosphere ? 



* The operation of this principle is seen when an oar, or any stick, 
is thrust into water. As the rays of light by which the oar is seen, have 
their direction changed as they pass out of water into air, the apparent 
direction in which the body is seen is changed in the same degree, 
giving it a bent appearance. Thus, in the figure, if Sax represents- the 
oar, Sab will be the bent appearance as affected by refraction. The 
transparent substance through which any ray of light passes, is called 
a medium. It is a general fact in optics, that when light passes out of 
a rarer into a denser medium, as out of air into water, or out of space 
into air, it is turned towards a perpendicular to the surface of the me- 
dium, and when it passes out of a denser into a rarer medium, as out 
of water into air, it is turned from the perpendicular. In the above 
case the light, passing out of space into air, is turned towards the ra- 
dius of the earth, this being perpendicular to the surface of the atmos- 
phere; and it is turned more and more towards that radius the nearer 
it approaches to the earth, because the density of the air rapidly in- 
creases. 



40 



THE EARTH. 



69. When a body is in the zenith, since a ray of light 
from it enters the atmosphere at right angles to the re- 
fracting medium, it suffers no refraction. Consequently, 
the position of the heavenly bodies, when in the zenith, 
is not changed by refraction, while, near the horizon, 
where a ray of light strikes the medium very obliquely, 
and traverses the atmosphere through its densest part, 
the refraction is greatest. The following numbers, ta- 
ken at different altitudes, will show how rapidly refrac- 
tion diminishes from the horizon upwards. The amount 
of refraction at the horizon is 34' 00". At different ele- 
vations it is as follows : 



I Elevation. 


Refraction. 


Elevation. 


Refraction. 


0° 10' 


32 / 00" 


30° 


r 40" 


0° 20' 


30' 00" 


40° 


1' 09" 


1° 00' 


24' 25" 


45° 


0' 58" 


5° 00' 


10' 00" 


60° 


0' 33'' 


10° 00' 


5' 20" 


80° 


0' 10" 


20° 00' 


2 39' 


90° 


0' 00" 



From this table it appears, that while refraction at the 
horizon is 34 minutes, at so small an elevation as only 
10' above the horizon it loses 2 minutes, more than the 
entire change from the elevation of 30° to the zenith. 
From the horizon to 1° above, the refraction is dimin- 
ished nearly 10 minutes. The amount at the horizon, 
at 45°, and at 90°, respectively, is 34', 58", and 0. In 
finding the altitude of a heavenly body, the effect of pa- 
rallax must be added, but that of refraction subtracted. 

70. Since the whole amount of refraction near the 
horizon exceeds 33', and the diameters of the sun and 
moon are severally less than this, these luminaries are in 



69. Has refraction any effect on a body in the zenith 1 Why 
not ? When is the refraction greatest ? What is the amount 
of refraction at the horizon ? How much does it lose within 
10' of the horizon ? What is the amount of refraction at an 
elevation of 45° ? 



REFRACTION. 41 

view both before they have actually risen and after they 
have set. 

The rapid increase of refraction near the horizon, is 
strikingly evinced by the oval figure which the sun as- 
sumes when near the horizon, and which is seen to the 
greatest advantage when light clouds enable us to view 
the solar disk. Were all parts of the sun equally raised 
by refraction, there would be no change of figure ; but 
since the lower side is more refracted than the upper, 
the effect is to shorten the vertical diameter and thus to 
give the disk an oval form. This effect is particularly 
remarkable when the sun, at his rising or setting, is ob- 
served from the top of a mountain, or at an elevation 
near the sea shore ; for in such situations the rays of 
light make a greater angle than ordinary, with a perpen- 
dicular to the refracting medium, and the amount of re- 
fraction is proportionally greater. In some cases of this 
kind, the shortening of the vertical diameter of the sun 
has been observed to amount to 6 7 , or about one fifth of 
the whole. 

71. The apparent enlargement of the sun and moon 
in the horizon, arises from an optical illusion. These 
bodies in fact are not seen under so great an angle when 
in the horizon, as when on the meridian, for they are 
nearer to us in the latter case than in the former. The 
distance of the sun is indeed so great that it makes very 
little difference in his apparent diameter, whether he is 
viewed in the horizon or on the meridian ; but with the 
moon the case is otherwise ; its angular diameter, when 
measured with instruments, is perceptibly larger at the 
time of its culmination. Why then do the sun and 
moon appear so much larger when near the horizon? It 



70. What effect has refraction upon the appearances of the 
sun and moon when near rising or setting ? Explain the oval 
figure of the sun when near the horizon. In what position of 
the spectator does this phenomenon appear most conspicuous? 
How much has the vertical diameter of the sun ever appeared 
to re shortened I 

4* 



42 THE EARTH. 

is owing to that general law, explained in optics, by 
which we judge of the magnitudes of distant objects, 
not merely by the angle they subtend at the eye, but 
also by our impressions respecting their distance, allow- 
ing, under a given angle, a greater magnitude as we im- 
agine the distance of a body to be greater. Now, on ac- 
count of the numerous objects usually in sight between 
us and the sun, when on the horizon, he appears much 
farther removed from us than when on the meridian, and 
we assign to him a proportionally greater magnitude. If 
we view the sun, in the two positions, through smoked 
glass, no such difference of size is observed, for here no 
objects are seen but the sun himself. 

The extraordinary enlargement of the sun or moon, 
particularly the latter, when seen at its rising through a 
grove of trees, depends on a different principle. Through 
the various openings between the trees, we see differ- 
ent images of the sun or moon, a great number of which 
overlapping each other, swell the dimensions of the 
body under the most favourable circumstances, to a very 
unusual size. 

TWILIGHT. 

72. Twilight also is another phenomenon depending 
upon the agency of the earth's atmosphere. It is that 
illumination of the sky which takes place just before 
sunrise, and which continues after sunset. It is due 
partly to refraction and partly to reflexion, but mostly to 
the latter. While the sun is within 18° of the horizon, 
before it rises or after it sets, some portion of its light is 
conveyed to us by means of numerous reflections from 



71. To what is the apparent enlargement, of the sun and 
moon when near the horizon owing ? Are these bodies seen 
under a greater angle when in the horizon than in the zenith 1 
To what general law of optics is the enlargement to be ascri- 
bed 1 How is it when we view the sua through smoked glass ? 
To what is the extraordinary enlargement of these luminaries 
owing, when seen through a grove of trees 1 




the atmosphere. Let AB (Fig. 9,) be the horizon of 
the spectator at A, and let SS be a ray of light from the 
sun when it is two or three degrees below the horizon. 
Then to the observer at A, the segment of the atmos- 
phere ABS would be illuminated. To a spectator at C, 
whose horizon was CD, the small segment SDa; would 
be the twilight ; while, at E, the twilight would disap- 
pear altogether. 

73. At the equator, where the circles of daily motion 
aie perpendicular to the horizon, the sun descends 
through 18° in an hour and twelve minutes (-ff=lih-)> 
and the light of day therefore declines rapidly, and as 
rapidly advances after day break in the morning. At the 
pole, a constant twilight is enjoyed while the sun is 
within 18° of the horizon, occupying nearly two-thirds 
of the half year when the direct light of the sun is with- 
drawn, so that the progress from continual day to con- 



72. Define twilight — How many degrees below the horizon 
is the sun when it begins and ends ? How is the light of the 
sun conveyed to us ? Explain by the figure. 

73. What is the length of twilight at the equator ? How 
long does it last at the poles ? How is the progress from con- 
tinual day to constant night? To the inhabitants of an oblique 
sphere, in what latitudes is twilight longest ? 



44 THE EARTH. 

stant night is exceedingly gradual. To the inhabitants 
of an oblique sphere, the twilight is longer in proportion 
as the place is nearer the elevated pole. 

74. Were it not for the power the atmosphere has of 
dispersing the solar light, and scattering it in various di- 
rections, no objects would be visible to us out of direct 
sunshine ; every shadow of a passing cloud would be 
pitchy darkness ; the stars would be visible all day, and 
every apartment into which the sun had not direct ad- 
mission, would be involved in the obscurity of night. 
This scattering action of the atmosphere on the solar 
light, is greatly increased by the irregularity of tempera- 
ture caused by the sun, which throws the atmosphere 
into a constant state of undulation, and by thus bringing 
together masses of air of different temperatures, produces 
partial reflections and refractions at their common boun- 
daries, by which means much light is turned aside from 
the direct course, and diverted to the purposes of general 
illumination. In the upper regions of the atmosphere, 
as on the tops of very high mountains, where the air is 
too much rarefied to reflect much light, the sky assumes 
a black appearance, and stars become visible in the day 
time. 



CHAPTER IV 

OF TIME. 



75. Time is a measured portion of indefinite duration* 
The great standard of time is the period of the revo- 
lution of the earth on its axis, which, by the most exact 



74. What would happen were it not for the power the at- 
mosphere has of dispersing the solar light ? What would every 
shadow of a cloud produce ? How is the scattering action of 
the atmosphere increased ? What is the aspect of the sky in 
the upper regions of the atmosphere ? 

* From old Eternity's mysterious orb, 

Was Time eiu off and cast beneath the skies. — Young 



TIME. 45 

observations, is found to be always the same. The time 
of the earth's revolution on its axis is called a sidereal 
day, and is determined by the revolution of a star from 
the instant it crosses the meridian, until it comes round 
to the meridian again. This interval being called a si- 
dereal day, it is divided into 24 sidereal hours. Obser- 
vations taken upon numerous stars, in different ages of 
the world, show that they all perform their diurnal rev- 
olutions in the same time, and that their motion during 
any part of the revolution is perfectly uniform. 

76. Solar time is reckoned by the apparent revolution 
of the sun, from the meridian round to the same meridian 
again. Were the sun stationary in the heavens, like a 
fixed star, the time of its apparent revolution would be 
equal to the revolution of the earth on its axis, and the 
solar and the sidereal days would be equal. But since 
the sun passes from west to east, through 360° in 365A 
days, it moves eastward nearly 1° a day, (59' 8".S). 
While, therefore, the earth is turning round on its axis, 
the sun is moving in the same direction, so that when 
we have come round under the same celestial meridian 
from which we started, we do not find the sun there, 
but he has moved eastward nearly a degree, and the 
earth must perform so much more than one complete 
revolution, in order to come under the sun again. Now 
since a place on the earth gains 359° in 24 hours, how 
long will it take to gain 1° 1 

24 

359 : 24 : : 1 : g7g=4m nearly. 



75. Deline time — What is the standard of time ? What is 
a sidereal day ? Do the stars all perform their revolutions in 
the same time ? Is their motion uniform ? 

76. How is the solar time reckoned? How far does the sun 
move eastward in a day ? How much longer is the solar than the 
sidereal day ? If we reckoned the sidereal day 24 hours, how 
should we reckon the solar? Reckoning the solar day at 24 
hours, how long is the sidereal ? 



46 THE EARTH. 

Hence the solar day is about 4 minutes longer than 
the sidereal ; and if we were to reckon the sidereal day 
24 hours, we should reckon the solar day 24h. 4m. To 
suit the purposes of society at large, however, it is found 
most convenient to reckon the solar day 24 hours, and to 
throw the fraction into the sidereal day. Then, 

24h 4m. : 24 : : 24 : 23h. 56m. nearly (23h. 56 in 4*.09) 
rrthe length of a sidereal day. 

77. The solar days, however, do not always differ from 
the sidereal by precisely the same fraction, since the in- 
crements of right ascension, which measure the differ- 
ence between a sidereal and a solar day, are not equal to 
each other. Apparent time, is time reckoned by the 
revolutions of the sun from the meridian to the meridian 
again. These intervals being unequal, of course the 
apparent solar days are unequal to each other. 

78. Mean time, is time reckoned by the average 
length of all the solar days throughout the year. This 
is the period which constitutes the civil day of 24 hours, 
beginning when the sun is on the lower meridian, name- 
ly, at 12 o'clock at night, and counted by 12 hours from 
the lower to the upper culmination, and from the upper 
to the lower. The astronomical day is the apparent so- 
lar day counted through the whole 24 hours, instead of 
by periods of 12 hours each, and begins at noon. Thus 

10 days and 14 hours of astronomical time, would be 

1 1 days and 2 hours of apparent time ; for when the 10th 
astronomical day begins, it is 10 days and 12 hours of 
civil time. 

79. Clocks are usually regulated so as to indicate mean 
solar time ; yet as this is an artificial period, not marked 



77. Do the solar days always differ from the sidereal by the 
same quantity 1 Define apparent time. 

78. Define mean time. What constitutes the civil day 1 
What makes an astronomical day 1 When does the civil day 
begin \ When does the astronomical day begin 1 



THE CALENDAR. 47 

off, like the sidereal day, by any natural event, it is ne- 
cessary to know how much is to be added to or sub- 
tracted from the apparent solar time, in order to give the 
corresponding mean time. The interval by which ap- 
parent time differs from mean time, is called the equation 
of time. If a clock were constructed (as it may be) so 
as to keep exactly with the sun, going faster or slower 
according as the increments of right ascension were 
greater or smaller, and another clock were regulated to 
mean time, then the difference of the two clocks, at any 
period, would be the equation of time for that moment. 
If the apparent clock were faster than the mean, then 
the equation of time must be subtracted ; but if the ap- 
parent clock were slower than the mean, then the equa- 
tion of time must be added, to give the mean time. 
The two clocks would differ most about the 3d of No- 
vember, when the apparent time is 16 T m greater than the 
mean (16 m 16 s .7). But, since apparent time is some- 
times greater and sometimes less than mean time, the 
two must obviously be sometimes equal t$ each other. 
This is in fact the case four times a year, namely, April 
15th, June 15th, September 1st, and December 24th. 

THE CALENDAR. 

80. The astronomical year is the time in which the 
sun makes one revolution in the ecliptic, and consists of 
365d. 5h. 48m. 51 s - 60. The civil year consists of 365 
days. The difference is nearly 6 hours, making one day 
in four years. 

The most ancient nations determined the number of 
days in the year by means of the stylus, a perpendicular 



79 What time do clocks commonly keep ? Define the equa- 
tion of time. How might two clocks be regulated so that their 
difference would indicate the equation of time ? How must 
the equation of time be applied when the apparent clock is 
faster than the mean ? How when it is slower ? When would 
the two clocks differ most 1 How much would they then differ 7 
When would they come together 1 



48 # THE EARTH 

rod which casts its shadow on a smooth plane, bearing a 
meridian line. The time when the shadow was shortest, 
would indicate the day of the summer solstice ; and the 
number of days which elapsed until the shadow returned 
to the same length again, would show the number of 
days in the year. This was found to be 365 wn»: ie 
days, and accordingly this period was adopted for tne 
civil year. Such a difference, however, between the 
civil and astronomical years, at length threw all dates 
into confusion. For, if at first the summer solstice hap- 
pened on the 21st of June, at the end of four years, the 
sun would not have reached the solstice until the 22d of 
June, that is, it would have been behind its time. At 
the end of the next four years the solstice would fall on 
the 23d ; and in process of time it would fall succes- 
sively on every day of the year. The same would be 
true of any other fixed date. Julius Caesar made the 
first correction of the calendar, by introducing an inter- 
calary day every fourth year, making February to con- 
sist of 29 instead of 28 days, and of course the whole 
year to consist of 366 days. This fourth year was de- 
nominated Bissextile. It is also called Leap Year. 

81. But the true correction was not 6 hours, but 5h. 
49m. ; hence the intercalation was too great by 11 min- 
utes. This small fraction would amount in 100 years 
to f of a day, and in 1000 years to more than 7 days. 
From the year 325 to 1582, it had in fact amounted to 
about 10 days ; for it was known that in 325, the vernal 
equinox fell on the 21st of March, whereas, in 1582 it 
fell on the 11th. In order to restore the equinox to the 
same date, Pope Gregory XIII, decreed, that the year 



80. Define the astronomical year — What is its exact period? 
Of how many days does the civil year consist? How much 
shorter is the civil than the astronomical year ? How did the most 
ancient nations determine the number of days in the year ? 
When would the stylus mark the shortest day and when the 
longest ? Explain the confusion which arose by reckoning the 
yearonly 365 days. How did Julius Caesarreform the calendar ? 



THE CALENDAR 49 

snould be brought forward 10 days, by reckoning the 
5th of October the 15th. In order to prevent the cal- 
endar from falling into confusion afterwards, the follow- 
ing rule was adopted : 

Every year whose number is not divisible by 4 with- 
out a remainder ■, consists of 365 days ; every year which 
is so divisible, but is not divisible by 100, of 366; every 
year divisible by 100 but not by 400, again of 365; and 
every year divisible by 400, of 366. 

Thus the year 1838, not being divisible by 4, contains 
365 days, while 1836 and 1840 are leap years. Yet to 
make every fourth year consist of 366 days would in- 
crease it too much by about f of a day in 100 years ; 
therefore every hundredth year has only 365 days. 
Thus 1800, although divisible by 4 was not a leap year, 
but a common year. But we have allowed a whale day 
in a hundred years, whereas w r e ought to have allowed 
only three fourths of a day. Hence, in 400 years we 
should allow a day too much, and therefore we let the 
400th year remain a leap year. This rule involves an 
error of less than a day in 4237 years. If the rule were 
extended by making every year divisible by 4000 (which 
would now consist of 366 days) to consist of 365 days, 
the error would not be more than one day in 100,000 
years. 

82. This reformation of the calendar was not adopted 
in England until 1752, by which time the error in the 
Julian calendar amounted to about 1 1 days. The year 
was brought forward, by reckoning the 3d of September 
the 14th. Previous to that time the year began the 25th 



81. By how many minutes was the allowance made by the 
Julian calendar too great ? To how much would the error 
amount m one hundred years ? To how much in a thousand 
years ? To how much had it amounted from the year 325 to 
1582 ? What changes did Pope Gregory make in the year? 
State the rule for the calendar. Of the three years 1836, 
1838, and 1840, which are leap years ? Was 1800 a leap year? 
How is every 400th year ? 

5 



50 THE EARTH. 

of March ; but it was now made to begin on the 1st oi 
January, thus shortening the preceding year, 1751, one 
quarter.* 

As in the year 1582, the error in the Julian calendar 
amounted to 10 days, and increased by f of a day in a 
century, at present the correction is 12 days ; and the 
number of the year wiM differ by one with respect to 
dates between the 1st of January and the 25th of March. 

Examples. General Washington was born Feb. 11 
1781, old style ; to what date does this correspond in 
new style ? 

As the date is the earlier part of the 18th century, the 
correction is 1 1 days, which makes the birth day fall on 
the 22d of February; and since the year 1731 closed 
the 25th of March, while according to new style 1732 
would have commenced on the preceding 1st of Janu- 
ary ; therefore, the time required is Feb. 22, 1732. It 
is usual, in such cases, to write both years, thus : Feb. 
11, 1731-2, O. S. 

2. A great eclipse of the sun happened May 15th, 
1 836 ; to what date would this time correspond in old 
style 1 Ans. May 3d. 

83. The common year begins and ends on the same 
day of the week ; but leap year ends one day later in the 
week than it began. 

For 52x7 = 384 days; if therefore the year begins 
on Tuesday, for example, 364 days would complete 52 
weeks, and one day would be left to begin another week, 



82. When was this reformation first adopted in England ? 
How was the year brought forward 1 When did the year be- 
gin before that time 1 To how many days did the error amount 
in 1752 ? How many days are allowed at present between 
old and new style ? 



* Russia, and the Greek Church generally, adhere to the old style. 
fn order to make the Russian dates correspond to ours, we must add to 
them 12 days. France and other Catholic countries, adopted the Gre- 
gorian calendar soon after it was promulgated 



ASTRONOMICAL INSTRUMENTS 51 

and the following year would begin on Wednesday. 
Hence, any day of the month is one day later in the 
week than the corresponding day of the preceding year. 
Thus, if the 16th of November, 1838, falls on Friday, 
the 10th of November, 1837, fell on Thursday, and in 
1839 will fall on Saturday. But if leap year begins on 
Sunday, it ends on Monday, and the following year be- 
gins on Tuesday ; while any given day of the month is 
two days latei in the week than the corresponding date 
of the preceding year. 



CHAPTER V. 

OF ASTRONOMICAL INSTRUMENTS FIGURE AND DENSITY OF 

THE EARTH. 

84. The most ancient astronomers employed no in- 
struments of observation, but acquired their knowledge 
of the heavenly bodies by long continued and most at- 
tentive inspection with the naked eye. Instruments for 
measuring angles were first used in the Alexandrian 
school, about 300 years before the Christian era. 

85. Wherever we are situated on the earth we appear 
to be in the center of a vast sphere, on the concave sur- 
face of which all celestial objects are inscribed. If we 
take any two points on the surface of the sphere, as two 
stars for example, and imagine straight lines to be drawn 
to them from the eye, the angle included between these 



83. If the common year begins on a certain day of the week, 
how will it end ? How is it with leap year ? How does any 
day of the month compare in the preceding and following yeai 
with respect to the day of the week 1 How is this in leap 
year ? 

84. How did the most ancient nations acquire their knowl- 
edge of the heavenly bodies ? When were astronomical in- 
struments first introduced 1 



52 THE EARTH. 

lines will be measured by the arc of the sky contained 
between the two points. Thus if HBD, (Fig. 10,) rep- 
Fig. 10. 




resents the concave surface of the sphere, A, B, two 
points on it, as two stars, and CA, CB, straight lines 
drawn from the spectator to those points, then the angu- 
lar distance between them is measured by the arc AB, 
or the angle ACB. But this angle may be measured on 
a much smaller circle, having the same center, as EFG, 
since the arc EF will have the same number of degrees 
as the arc AB. The simplest mode of taking an angle 
between two stars, is by means of an arm opening at a 
joint like the blade of a penknife, the end of the arm 
moving like CE upon the graduated circle KEG. 

The common surveyor's compass affords a simple ex- 
ample of angular measurement. Here the needle lies in 
a north and south line, while the circular rim of the 
compass, when the instrument is level, corresponds to 
the horizon. Hence the compass shows how many de- 
grees any object to which we direct the eye, lies east or 
west of the meridian. 



85. How is the angular distance between two points on the 
celestial sphere measured ? Explain figure 10, Show how the 
circles of the sphere may be truly represented by the smaller 
circles of the instrument, as the horizon by the surveyor's com- 
pass. Explain the simplest mode of taking angles by figure 10 



ASTRONOMICAL INSTRUMENTS. 53 

86. It is obvious that the larger the graduated circle 
is, the more minutely its limb may be divided. If the 
circle is one foot in diameter, each degree will occupy 
£o of an inch. If the circle is 20 feet in diameter, a 
degree will occupy the space of two inches and could 
be easily divided to minutes, since each minute would 
cover a space of ^ of an inch. Refined astronomical 
circles are now divided with very great skill and accu- 
racy, the spaces between the divisions being, when read 
off, magnified by a microscope ; but in former times, 
astronomers had no mode of measuring small angles 
but by employing very large circles. But the telescope 
and microscope enable us at present to measure celestial 
arcs much more accurately than was done by the older 
astronomers. 

The principal instruments employed in astronomy, 
are the Telescope, the Transit Instrument, the Altitude 
and Azimuth Instrument, and the Sextant. 

87. The Telescope has greatly enlarged our knowl- 
edge of astronomy, both by revealing to us many things 
invisible to the naked eye, and also by enabling us to 
attain a much higher degree of accuracy than we could 
otherwise reach, in angular measurements. It was in- 
vented by Galileo about the year 1600. The powers of 
the telescope were improved and enlarged by successive 
efforts, and finally, about 50 years ago, telescopes were 
constructed in England by Dr. Herschel, of a size and 
power that have not since been surpassed. 

A complete knowledge of the telescope cannot be ac- 
quired without an acquaintance with the science of op- 
tics ; but we may perhaps convey to one unacquainted 
with that science, some idea of the leading principles of 



86. What is the advantage of having large circles for angu- 
lar measurements ? When the circle is one foot in diameter, 
what space will 1° occupy on the limb 1 What space when 
the circle is twenty feet in diameter ? What are the princi- 
pal instruments used in astronomical observations 1 



54 



THE EARTH. 



this noble instrument. By means of the telescope, we 
first form an image of a distant object as the moon for 
example, and then magnify that image by a microscope. 
Let us first see how the image is formed. This may be 
done either by a convex lens, or by a concave mirror. A 
convex lens is a flat piece of glass, having its two faces 
convex, or spherical, as is seen in a common sun glass. 
Every one who has seen a sun glass, knows that when 
held towards the sun it collects the solar rays into a 
small bright circle in the focus. This is in fact a small 
image of the sun. In the same manner the image of 
any distant object, as a star, may be formed as is repre- 
sented in the following diagram. Let ABCD represent 
Fig. 11. 




the tube of a telescope. At the front end, or at the end 
which is directed towards the object, (which we will 
suppose to be the moon,) is inserted a convex lens, 
L, which receives the rays of light from the moon, and 
collects them into the focus at a, forming an image of 
the moon. This image is viewed by a magnifier attach- 
ed to the end BC. The lens L is called the object-glass, 
and the microscope in BC the eye-glass. We apply a 
magnifier to this image just as we would to any object ; 



87. Who invented the telescope ? Who constructed tele- 
scopes of great size and power ? Explain tne leading prin- 
ciple of the telescope. How is the image formed 1 What is 
a convex lens ? How does it affect parallel rays of light ? 
How do we view the image formed by the lens ? How is the 
image magnified 1 How is it rendered brighter ? 



ASTRONOMICAL INSTRUMENTS. 5f» 

and by greatly enlarging its dimensions, we may render 
its various parts far more distinct than they would other- 
wise be, while at the same time the object lens collects 
and conveys to the eye a much greater quantity of light 
than would proceed directly from the body under exam- 
ination. A very small beam of light only from a distant 
object, as a star, can enter the eye directly ; but a lens 
one foot in diameter will collect a beam of light of the 
same dimensions, and convey it to the eye. By these 
means many obscure celestial objects become distinctly 
visible, which w r ould otherwise be either too minute, or 
not sufficiently luminous to be seen by us. 

88. But the image may also be formed by means of a 
concave mirror, w T hich, as well as the convex lens, has 
the property of collecting the rays of light which pro- 
ceed from any luminous body, and of forming an image 
of that body. The image formed by the concave mir- 
ror is magnified by a microscope in the same manner as 
when formed by the convex lens. When the lens is 
used to form an image, the instrument is called a Re- 
fracting telescope ; when a concave mirror is used, it is 
called a Reflecting telescope. 

The telescope in its simplest form is employed not so 
much for angular measurements, as for aiding the pow- 
ers of vision in viewing the celestial bodies. When di- 
rected to the sun, it reveals to us various irregularities on 
his disk not discernible by naked vision ; w T hen turned 
upon the moon or the planets, it affords us new and in- 
teresting views, and enables us to see in them the linea- 
ments of other worlds ; and w r hen brought to bear upon 
the fixed stars, it vastly increases their number and re- 
veals to us many surprising facts respecting them. 



88. How is an image formed by a concave mirror 1 How is 
this image magnified 1 When is the instrument called a re- 
fracting and when a reflecting telescope I For what pur- 
poses are telescopes chiefly employed ? 



56 



THE EARTH. 



89. The Transit Instrument is a telescope, which is 
fixed permanently in the meridian, and moves only in 
that plane. It rests on a horizontal axis, which consists 
of two hollow cones applied base to base, a form uniting 
lightness and strength. The two ends of the axis rest 
Fig. 12. 




TV 



on two firm supports, as pillars of stone, for example, so 
connected with the building as to be as free as possible 
from all agitation. In figure 12, AD represents the tele- 



89. What is a Transit Instrument ? On what supports does 
it rest as represented in figure 12. Why are they made so firm? 
Describe all parts of the instrument. What is its use 1 How 
used to regulate clocks and watches ? What kind of time is 
shown when the sun is on the meridian ? How is this con- 
verted into mean t'me ? Give an example. 



ASTRONOMICAL INSTRUMENTS. 57 

scope, E, W, massive stone pillars supporting the hori- 
zontal axis, beneath which is seen a spirit level, (which 
is used to bring the axis to a horizontal position,) and n 
a vertical circle graduated into degrees and minutes. 
This circle serves the purpose of placing the instrument 
at any required altitude, or distance from the zenith, and 
of course for determining altitudes and zenith distances. 
The use of the transit instrument is to show the pre- 
cise moment when a heavenly body is on the meridian. 
One of its uses is to enable us to obtain the true time, 
and thus to regulate our clocks and watches. We find 
when the sun's center is on the meridian, and this gives 
us the time of noon or apparent time. (Art. 78.) But 
watches and clocks usually keep mean time, and there- 
fore in order to set our time piece by the transit instru- 
ment, we must apply the equation of time. 

90. A noon mark may easily be made by the aid of 
the Transit Instrument. A window sill is frequently 
selected as a suitable place for the mark, advantage be- 
ing taken of the shadow projected upon it by the per- 
pendicular casing of the window. Let an assistant stand 
with a rule laid on the line of shadow and with a knife 
ready to make the mark, the instant when the observer 
at the Transit Instrument announces that the center of 
the sun is on the meridian. By a concerted signal, as 
the stroke of a bell, the inhabitants of a town may all 
fix a noon mark from the same observation. It must be 
borne in mind, however, that the noon mark gives the 
apparent time, and that the equation of time must be 
allowed for in setting the clock or watch. Suppose we 
wish to set our clock right on the first of January. We 
find by a table of the equation of time, that mean time 
then precedes apparent time 3m. 43s. ; we must there- 
fore set the clock at 3m. 43s. the instant the center of 
the sun is on the meridian. If the time had been the 
first of May instead of the first of January, then we 
find by the table that 3m. is to be subtracted from the 
apparent time, and consequently, when the center of the 

90 Describe the mode of making a noon mark. 



58 



THE EARTH. 



sun was on the meridian, we should set our clock at 1 lh. 
57m. or 3m. before twelve. 



91. The equation of time varies a little with different 
years, but the following table will always be found 
within a few seconds of the truth. The equation for 
the current year is given exactly in the American Al- 
manac. 

Equation of Time for Apparent Noon. 





Jan. 1 Feb. 


Mar. 'Apr. 


May 
Sub. 

M. S. 


JUN. 

Sub. 

M. S 


Jul. 
Add. 


Aug 
Add. 


Sept. 
Add. 


Oct. 
Sub. 
M. s. 


Nov. 
Sub. 


Sub. 

M. S/. 


Add. 

M. S. 


Add. 


Add. 


Add. 


M. S. 


M. S. 


M. S. 


M. S. 


M. S. 


M. S. 


M. S. 


l 


3.4313.53 


12.42 


4. "7; 


3. 2.38 


3.19 


6. 3 


ai). 1 


10. 9 


16.15 


10.54 


2 


4.1l|l4. 1 


12.30 


3.48 


3. 7 2.29 


3.31 


5.59 


50.17 


10.28 


16.16 


10.32 


3 


4.39;i4. 8 


12.18 


3.30 


3.15 


2.19 


3.42 


5 55 


0.36 


10.47 


16.17 


10. 8 


4 


5. 744.14 


12. 5 


3.12 


3.21 


2.10 


3.53 5.50 


0.56 


11. 6 


16.17 


9.45 


5 


5.3414.19 


11.51 


2.54 
2.37 


3.27 
3.32 


2. 
1.49 


4. 4 


5.45 


1.15 


11.24 


16.16 


9.20 


6. 1)14.24 


11.38 


4.15 


5.3<J 


1.35 


11.42 


1614 


8.55 


7 


6.27114.27 


11.23 


2.19 


3.37 


1.39 


4.25 


5.33 


1.55 


11.59 


16.11 


8.30 


R 


6.53|14.30 


11. 8 


2. 2 


3.42 


1.28 


4.34 


5.25 


2.15 


12.16 


16. 7 


8. 4 


9 


7.18.14.32 


10.53 


1.45 


3.46 


1.17 


4.44 


5.18 


2.36 


12.33 16. 3 


7.37 


10 
11 


743; 14.33 


10.38 


1.28 
1.11 


3.49 
3.51 


1. 5 

0.53 


4.53 
5. 1 


5. 9 
5. 1 


2.56 


12.49 15.58 
13. 515 51 


7.10 


8. 7 14.34 


10.22 


3.17 


6.43 


12 


8.3114.33 


10. 6 


0.55 


3.53 


0.41 


5. 9 


4.51 


3.38 


13.20 


15.44 


6.15 


13 


8.5414.32 


9.49 


0.39 


3.55 


0.29 


5.17 


4.41 


3.59 


13.34 


15.37 


5.47 


L4 


9.1614.30 


9.32 


0.23 


3.56 


0.17 


5.24 


4.31 


4.2013.49 15.28 


5.18 


15 


9.37 


14.28 


9.15 


0. 8 


3.56 


0. 4 


5.30 


4.20 


4.41 


14. 215.18 


4.49 










Sub. 




Add. 














16 


9.5814.25 


8.581 


0. 7 


3.56 


0. 8 


5.37 


4. 8 


5. 2 


14.15 


15. 8 


4.20 


17 


10.19il4.20 


8.41 


0.22 


3.55 


0.21 


5.42 


3.56 


5.23 


14.28 


14.56 


3.50 


IS 


10.3814.16 


8.23 


0.36 


3.54 


0.34 


5.48 


3.44 


5.44 


14.39 


14.44 


3.21 


19 


10.5714.10 


8. 5 


0.50 


3.52 


0.47 


5.52 


3.31 


6. 514.51 


14.31 


2.51 


•20 
21 


11.1514. 4 


7.47 


1. 3 


3.49 
3.46 


1. 
1.13 


5.57 
6. 


3.17 
3. 3 


6.26 
'6.47 


15. 1|14.17 


2.21 


11.33113.58 


7.29 


1.16 


15.11J14. 3 


1.51 


22 


11.49113.50 


7.11 


1.29 


3.42 


1.26 


6. 3 2.49 


7. 8115.21:13.47 


1.21 


23 


12. 513.42 


6.52 


1.41 


3.38 


1.39 


6. 6 


2.34 


7.29 15.29J13.31 

7.4915.37113.14 


0.51 


24 


12.2013.34 


6.34 


1.52 


3.33 


1.52 


6. 8 


2.19 


0.21 


25 
2G 


12.3513.25 


6.15 


2. 4 


3.28 
3.22 


2. 5 

2.18 


6. 9 
6.10 


2. 3 


8.1015.4412.56 


«0. 9 


12.4813.15 


5.57 2,14 


1.47 


8.30115.51 12.38 
8.5015.57il2.18 


0.39 


27 


13. 1 13. 4 


5.38 


2.24 


3.16 


2.30 


6.10 


1.30 


1. 9 


28 


13.13 


12.54 


5.20 


2.34 


3. 9 


2.43 


6.10 


1.13 


9.1116. 211.58 


1.39 


29 


13.24 




5. 1 


2.43 


3. 2 


2.55 


6. 9 

6. 8 


0.5G 


9.3016. 6,11.38 


2. 8 


30 
31 


13.35 




4.43 


2.52 


2 54 


3. 8 


0.38 


9.50.16.1011.16 


2.37 


13.44 




4.25 




2.46 




6. 5 


0.20 


116.13 


3. 6 



91. Is the equation of time the same or different in different 
years ? In what book mav it. be found exactly for the cur- 
rent year ? 



ASTRONOMICAL INSTRUMENTS. 59 

92. The Astronomical Clock is the constant compan- 
ion of the Transit Instrument. This clock is so regu- 
lated as to keep exact pace with the stars, and of course 
with the revolution of the earth on its axis ; that is, it 
is regulated to sidereal time. It measures the progress 
of a star, indicating an hour for every 15°, and 24 hours 
for the whole period of the revolution of the star. Si- 
dereal time, it will be recollected, commences when the 
vernal equinox is on the meridian, just as solar time com- 
mences when the sun is on the meridian. Hence, the 
hour by the sidereal clock has no correspondence with 
the hour of the day, but simply indicates how long it is 
since the equinoctial point crossed the meridian. For 
example, the clock of an observatory points to 3h 20m. ; 
this may be in the morning, at noon, or any other time 
of the day, since it merely shows that it is 3h. 20m. 
since the equinox was on the meridian. Hence, when 
a star is on the meridian, the clock itself shows its right 
ascension ; (Art. 24,) and the interval of time between 
the arrival of any two stars upon the meridian, is the 
measure of their difference of right ascension. 

93. Astronomical clocks are made of the best work- 
manship, with a compensation pendulum, and every 
other advantage which can promote their regularity. 
The Transit Instrument itself, when once accurately 
placed in the meridian, affords the means of testing the 
correctness of the clock, since one revolution of a star 
from the meridian to the meridian again, ought to cor- 
respond to exactly 24 hours by the clock, and to con- 



92. How is the astronomical clock regulated 1 What does 
it measure ? How many degrees does a star pass over in an 
hour ? When does sidereal time commence ? What is de- 
noted by the hour and minute of a sidereal clock 1 How do 
we determine the right ascension of a star ? 

93. How is the workmanship of astronomical clocks ? How 
is the correctness of a clock tested ? To what degree of 
perfection are clocks brought? By what instrument are 
clocks regulated? 



60 THE EARTH. 

tinue the same from day to day ; and the right ascen- 
sion of various stars as they cross the meridian, ought 
to be such by the clock as they are given in the tables, 
where they are stated according to the accurate determi- 
nations of astronomers. Or by taking the difference of 
right ascension of any two stars on successive days, it 
will be seen whether the going of the clock is uniform 
for that part of the day ; and by taking the right ascen- 
sion of different pairs of stars, we may learn the rate of 
the clock at various parts of the day. We thus learn, 
not only whether the clock accurately measures the 
length of the sidereal day, but also whether it goes uni- 
formly from hour to hour. 

Although astronomical clocks have been brought to a 
great degree of perfection, so as to vary hardly a second 
for many months, yet none are absolutely perfect, and 
most are so far from it as to require to be corrected by 
means of the Transit Instrument every few days. In- 
deed, for the nicest observations, it is usual not to at- 
tempt to bring the clock to an absolute state of correct- 
ness, but after bringing it as near to such a state as can 
conveniently be done, to ascertain how much it gains or 
loses in a day ; that is, to ascertain its rate of going, and 
to make allowance accordingly. 

94. The Transit Instrument is adapted to taking obser- 
vations on the meridian only ; but we sometimes require 
to know the altitude of a celestial body when it is not 
on the meridian, and its azimuth, or distance from the 
meridian measured on the horizon. An instrument es- 
pecially designed to measure altitudes and azimuths, is 
called an Altitude and Azimuth Instrument, whatever 
may be its particular form. When a point is on the hor- 
izon its distance from the meridian, or its azimuth, may 
be taken by the common surveyor's compass, the direc- 



94. To what kind of observations only is the transit instru- 
ment adapted ? What instrument is employed for finding alti- 
tude and azimuth 1 Describe the Altitude and Azimuth In- 
stalment; from fisrure 13. 



ASTRONOMICAL INSTRUMENTS. 



61 



tion of the meridian being determined by the needle ; 
but when the object, as a star, is not on the horizon, its 
azimuth, it must be remembered, is the arc of the hori- 
zon from the meridian to a vertical circle passing through 
the star ; at whatever different altitudes, therefore, two 
stars may be, and however the plane which passes 
through them may be inclined to the horizon, still it is 
their angular distance measured on the horizon which 
determines their difference of azimuth. Figure 13 rep- 
resents an Altitude and Azimuth Instrument, several of 
the usual appendages and subordinate contrivances being 
omitted for the sake of distinctness and simplicity. Here 
abc is the vertical or altitude circle, and EFG the hori- 
zontal or azimuth circle ; AB is a telescope mounted on 

Fier. 13. 




a horizontal axis and capable of two motions, one in al- 
titude parallel to the circle abc, and the other in azimuth 
parallel 10 EFG. Hence it can be easily brought to 

6 



62 THE EARTH. 

bear upon any object. At m, under the eye glass of the 
telescope, is a small mirror placed at an angle of 45° 
with the axis of the telescope, by means of which the 
image of the object is reflected upwards, so as to be 
conveniently presented to the eye of the observer. At d 
is represented a tangent screw, by which a slow motion 
is given to the telescope at c. At h and g are seen two 
spirit levels, at right angles to each other, which show 
when the azimuth circle is truly horizontal. The in- 
strument is supported on a tripod, for the sake of greater 
steadiness, each foot being furnished with a screw for 
levelling. 

95. The Sextant is an instrument used for taking the 
angular distance between any two bodies on the surface 
of the celestial sphere, by reflecting the image of one of 
the bodies so as to coincide with the other body as seen 
directly. It is particularly valuable for measuring celes- 
tial arcs at sea, because it is not, like most astronomical 
instruments, affected by the motion of the ship. 

This instrument (Fig 14,) is of a triangular shape, 
and is made strong and firm by metallic crossbars. It 
has two reflectors, I and H, called, respectively, the Index 
Glass, and the Horizon Glass, both of which are firmly 
fixed perpendicular to the plane of the instrument. The 
Index Glass is attached to the movable arm ID and 
turns as this is moved along the graduated limb EF. 
This arm also carries a Vernier at D, which enables us to 
take off minute parts of the spaces into which the limb 
is divided. The Horizon Glass, H, consists of two 
parts ; the upper being transparent or open, so that the 
eye, looking through the telescope T, can see through 
it a distant body as a star at S, while the lower part is 
a reflector. 



95. Define the Sextant — For what is it particularly valu- 
able ? Describe it from figure 14. Where is the Vernier and 
what is its use ? Specify the manner in which the light comes 
from the object to the eye. How can we measure the angulai 
distance between the raoon and a star 1 



ASTRONOMICAL INSTRUMENTS. 



63 



Suppose it were required to measure the angular dis- 
tance between the moon and a certain star, the moon 

Fig. 14. 




being at M, and the star at S. The instrument is held 
firmly in the hand, so that the eye, looking through the 
telescope, sees the star S through the transparent part of 
the Horizon Glass. Then the movable arm ID is moved 
from F towards E, until the image of M is carried down 
to S, when the number of degrees and parts of a degree 
reckoned on the limb from F to the index at D, will 
show the angular distance between the two bodies. 



FIGURE AND DENSITY OP THE EARTH. 

96. We have already shown, that the figure of the 
earth is nearly globular ; but since the semi-diameter of 
the earth is taken as the base line in determining the 
parallax of the heavenly bodies, and lies therefore at the 
foundation of all astronomical measurements, it is very 



64 



THE EARTH. 



important that it should be ascertained with the greatest 
possible exactness. Having now learned the use of as- 
tronomical instruments, and the method of measuring 
arcs on the celestial sphere, we are prepared to under- 
stand the methods employed to determine the exact fig- 
ure of the earth. This element is indeed ascertained 
in different ways, each of which is independent of all 
the rest, namely, by investigating the effects of the cen- 
trifugal force arising from the revolution of the earth 
on its axis — by measuring arcs of the meridian — and by 
experiments with the pendulum. 



97. First, the known effects of the centrifugal force, 
would give to the earth a spheroidal figure, elevated in 
the equatorial, and fattened in the polar regions. 

By the centrifugal force is meant, the tendency which 
revolving bodies exhibit to recede from the 
Fig. 15. center. Thus when a grindstone is turn- 
iiiiiiiiiiiiiiiininiiiiiiiiiiiiiil ed swiftly, water is thrown off from it in 
straight lines. The same effect is notic- 
ed when a carriage wheel is driven rapidly 
through the water. If a pail, containing 
a little water, is whirled, the water rises 
on the sides of the pail in consequence of 
the centrifugal force. The same principle 
is more strikingly illustrated by the annex- 
ed cut, (Fig. 15,) which represents an 
open glass vessel suspended by a cord at- 
tached to its opposite sides, and passed 
through a staple in the ceiling of the room. 
A little water is introduced into the ves- 
sel which is made to whirl rapidly by ap- 
plying the hand to the opposite sides. As 
it turns, the water rises on the sides of the 
vessel, receding as far as possible from the 




96. Why is it so necessary to ascertain accurately the semi- 
diameter of the earth 1 In how many different ways is this 
element ascertained 1 Specify them. What is meant by the 
centrifugal force 1 Give an illustration. Describe figure 15. 



ASTRONOMICAL INSTRUMENTS. 65 

center. The same effect is produced by suffering the 
cord to untwist freely, which gives a swift revolution 
to the vessel. In like manner, a ball of soft clay when 
made to turn rapidly on its axis, swells out in the central 
parts and becomes flattened at the ends, forming the fig- 
ure called an oblate spheroid. 

Had the earth been originally constituted (as geolo- 
gists suppose) of yielding materials, either fluid or semi- 
fluid, so that its particles could obey their mutual at- 
traction, while the body remained at rest it would spon- 
taneously assume the figure of a perfect sphere ; as soon, 
however, as it began to revolve on its axis, the greater 
velocity of the equatorial regions would give to them a 
greater centrifugal force, and cause the body to swell 
out into the form of an oblate spheroid. Even had the 
solid part of the earth consisted of unyielding materials 
and been created a perfect sphere, still the waters that 
covered it would have receded from the polar and have 
been accumulated in the equatorial regions, leaving bare 
extensive regions on the one side, and ascending to a 
mountainous elevation on the other. 

On estimating, from the known dimensions of the 
earth and the velocity of its rotation, the amount of the 
centrifugal force in different latitudes, and the figure of 
equilibrium which would result, Newton inferred that 
the earth must have the form of an oblate spheroid be- 
fore the fact had been established by observation ; and 
he assigned nearly the true ratio of the polar and equa- 
torial diameters. 



97. What would be the figure of the earth derived from the 
centrifugal force ? What figure would the earth have assumed 
if at rest 1 How would this figure be changed when it began to 
revolve ? Had the earth been originally a solid sphere covered 
with water, how would the water have disposed itself when the 
earth was made to turn on its axis ? How was the spheroidal 
figure of the earth inferred before the fact was established bv 
observation ? 

6* 



66 THE EARTH. 

98. Secondly, the spheroidal figure of the earth is 
proved, by actually measuring the length of a degree on 
the meridian in different latitudes. 

Were the earth a perfect sphere, the section of it made 
by a plane passing through its center in any direction 
would be a perfect circle, whose curvature would be 
equal in all parts ; but if we find by actual observation, 
that the curvature of the section is not uniform, we in- 
fer a corresponding departure in the earth from the figure 
of a perfect sphere. The task of measuring portions of 
the meridian, has been executed in different countries. 
We may know, in- each case, how far we advance on 
the meridian, because every step we take northward, 
produces a corresponding increase in the altitude of the 
north star. That an increase of the length of the de 
grees of the meridian, as we advance from the equator 
towards the pole, really proves that the earth is flattened 
at the poles, will be readily seen on a little reflection. 
We must bear in mind that a degree is not any certain 
length, but only the three hundred and sixtieth part of a 
circle, whether great or small. If, therefore, a degree is 
longer in one case than in another, we infer that it is the 
three hundred and sixtieth part of a larger circle ; and 
since we find that a degree towards the pole is longer 
than a degree towards the equator, we infer that the cur- 
vature is less in the former case than in the latter. 

The result of all the measurements is, that the length 
of a degree increases as we proceed from the equator 
towards the pole, as may be seen from the following 
table : 



98. By what measurements is the spheroidal figure of the 
earth proved ? What would be the curvature in all parts were 
the earth a perfect sphere ? How may we know when we have 
advanced one degree northward in the meridian ? Explain how 
an increase of the length of a degree proves that the earth is 
flattened towards the poles ? In what places have arcs of the me- 
ridian been measured ? What is the mean diameter of the 
earth I What is the difference between the two diameters ? 
What fraction expresses the ellipticity of the earth ? 



ASTRONOMICAL INSTRUMENTS. 



67 



Places of observation. 


Latitude. 


Length of a degree in miles 


Peru, 


00° 00' 00" 


68.732 


Pennsylvania, 


30 12 00 


68.896 


Italy, 


43 01 00 


68.998 


France, 


46 12 00 


69.054 


England, 


51 29 54J 


69.164 


Sweden, 


66 20 10 


69.292 



Combining the results of various estimates, the di- 
mensions of the terrestrial spheroid are found to be as 
follows : 

Equatorial diameter, . . . 7925.648 

Polar diameter, . . . . 7899.170 

Mean diameter, .... 7912.409 

The difference between the greatest and the least, is 
26.478 — 2 ^9 of the greatest. This fraction (^q) is de- 
nominated the ellipticity of the earth, being the excess 
of the longest over the shortest diameter. 

99. Thirdly, the figure of the earth is shown to be 
spheroidal, by observations with the pendulum. 

If a pendulum, like that of a clock, be suspended 
and the number of its vibrations per hour be counted, 
they will be found to be different in different latitudes. 
A pendulum that vibrates 3600 times per hour at the 
equator, will vibrate 3605J times at London, and a still 
greater number of times nearer the north pole. Now the 
vibrations of the pendulum are produced by the force of 



96. Explain how we may ascertain the figure of the earth by 
means of a pendulum — How will the number of vibrations be 
in different latitudes 1 How many times will a pendulum vi- 
brate in an hour at London, which vibrates 3600 times per hour 
at the equator 1 How are the vibrations of the pendulum pro- 
duced 1 Why are these comparative numbers at different 
places measures of the relative distances from the center of the 
earth ? What could we infer from two observations with the 
pendulum, one at the equator and the other at the north pole ? 
To what conclusions have pendulum observations, made in va- 
rious parts of the earth, led ? 



68 THE EARTH. 

gravity. Hence their comparative number at different 
places is a measure of the relative forces of gravity at 
those places. But when we know the relative forces of 
gravity at different places, we know their relative dis- 
tances from the center of the earth, because the nearer a 
place is to the center of the earth, the greater is the force 
of gravity. Suppose, for example, we should count the 
number of vibrations of a pendulum at the equator, and 
then carry it to the north pole and count the number of 
vibrations made there in the same time ; we should be 
able from these two observations to estimate the relative 
forces of gravity at these two points ; and having the rel- 
ative forces of gravity, we can thence deduce their rela- 
tive distances from the center of the earth, and thus ob- 
tain the polar and equatorial diameters. Observations 
of this kind have been taken with the greatest accuracy 
in many places on the surface of the earth, at various 
distances from each other, and they lead to the same 
conclusions respecting the figure of the earth, as those 
derived from measuring arcs of the meridian. 

100. The density of the earth compared with water, 
that is, its specific gravity, is 5^ c The density was first 
estimated by Dr. Hutton, from observations made by D v . 
Maskelyne, Astronomer Royal, on Schehallien, a moun- 
tain of Scotland, in the year 1774. Thus, let M (Fig. 
16,) represent the mountain, D, B, two stations on op- 
posite sides of the mountain, and I a star ; and let IE 
and IG be the zenith distances as determined by the 
difference of latitude of the two stations. But the ap- 
parent zenith distances as determined by the plumb line 
are IE' and IG'. The deviation towards the mountain 
on each side exceeded 7". The attraction of the moun- 
tain being observed on both sides of it, and its mass be- 
ing computed from a number of sections taken in all di- 



100 What is the specific gravity of the earth ? How was it 
ascertained? Explain figure 16. Why is the density of the 
earth so important an element ? 



DENSITY OF THE EARTH. 



69 




rections, tnese data, when compared with the known 
attraction and magnitude of the earth, led to a knowl- 
edge of its mean density. According to Dr. Hutton 
this is to that of water as 9 to 2 ; but later and more ac- 
curate estimates have made the specific gravity of the 
earth as stated above. But this density is nearly double 
the average density of the materials that compose the 
exterior crust of the earth, showing a great increase of 
density towards the center. 

The density of the earth is an important element, as 
we shall find that it helps us to a knowledge of the den- 
sity of each of the other members of the solar system. 



PART II. — OF THE SOLAR SYSTEM. 



101 Having considered the Earth, in its astronomical 
relations, and the Doctrine of the Sphere, we proceed 
now to a survey of the Solar System, and shall treat suc- 
cessively of the Sun, Moon, Planets, and Comets. 



CHAPTER I. 

OF THE SUN SOLAR SPOTS— ZODIACAL LIGHT. 

102. Tun figure which the sun presents to us is that 
of a perfect circle, whereas most of the planets exhibit a 
disk more or less elliptical, indicating that the true shape 
of the body is an oblate spheroid. So great, however, 
is the distance of the sun, that a line 400 miles long 
would subtend an angle of only l y/ at the eye, and would 
therefore be the least space that could be measured. 
Hence, were the difference between two conjugate di- 
ameters of the sun any quantity less than this, we could 
not determine by actual measurement that it existed at 
all. Still we learn from theoretical considerations, 
founded upon the known effects of centrifugal force, 
arising from the sun's revolution on his axis, that his 
figure is not a perfect sphere, but is slightly spheroidal. 

103. The distance of the sun from the earth, is nearly 
95,000,000 miles. In order to form some faint concep- 



101. What subjects are treated of in Part II 

102. What figure does the sun present to us ? What angle 
would a line of 400 miles on the sun's disk subtend ? How is 
it inferred that the figure of the sun is spheroidal 1 



DENSITY. 71 

tion at least of this vast distance, let us reflect that a rail- 
way car, moving at the rate of 20 miles per hour, would 
require more than 500 years to reach the sun. 

The apparent diameter of the sun is a little more than 
half a degree, (32' 3".) Its linear diameter is about 
885,000 miles ; and since the diameter of the earth is 
only 7912 miles, the latter, number is contained in the 
former nearly 112 times; so that it would require one 
hundred and twelve bodies like the earth, if laid side by 
side, to reach across the diameter of the sun ; and a ship 
sailing at the rate of ten miles an hour, would require 
more than ten years to sail across the solar disk. 

The sun is about 1,400,000 times as large as the earth. 
The distance of the moon from the earth being 238,000 
miles, were the center of the sun made to coincide with 
the center of the earth, the sun would extend every way 
from the earth nearly twice as far as the moon. 

1 04. In density, the sun is only one-fourth that of the 
earth, being but a little heavier than water ; and the 
quantity of matter in the. sun is three hundred and fifty 
thousand times as great as in the earth. A body would 
weigh nearly 28 times as much at the sun as at the 
earth. A man weighing 200 lbs. would, if transported 
to the surface of the sun, weigh 5,580 lbs., or nearly 2\ 
tons. To lift one's limb, would, in such a case, be be- 
yond the ordinary power of the muscles. At the surface 
of the earth, a body falls through lGjLfeet in a second; 



103. What is the distance of the sun from the earth 1 How 
long would a railway car, moving at the rate of 20 miles per 
hour, require to reach the sun ? How many bodies equal to 
the earth could lie side by side across the sun 1 How long 
would a ship be in sailing across it at 10 miles an hour ? If 
the sun's center were made to coincide with the center of the 
earth, how much farther would it reach than the moon ? What 
is the sun's apparent diameter 1 What is its linear diameter 1 

104. In density how does the sun compare with the earth? 
How in quantity of matter ? How much more would a body 
weigh at the sun than at the earth ? How far would a body 
fall in one second at the surface of the sun ? 



72 THE SUN. 

but a body would fall at the sun in one second through 
448.7 feet. 

SOLAR SPOTS. 

105. The surface of the sun, when viewed with a 
telescope, usually exhibits dark spots, which vary much, 
at different times, in number, figure, and extent. One 
hundred or more, assembled in several distinct groups, 
are sometimes visible at once on the solar disk. Tlje 
greatest part of the solar spots are commonly very small, 
but occasionally a spot of enormous size is seen occupy- 
ing an extent of 50,000 miles in diameter. They are 
sometimes even visible to the naked eye, when the sun 
is viewed through colored glass, or, when near the hori- 
zon, it is seen through light clouds or vapours. When it 
is recollected that 1" of the solar disk implies an extent 
of 400 miles, it is evident that a space large enough to be 
seen by the naked eye, must cover a very large extent. 

A solar spot usually consists of two parts, the nucleus 
and the umbra, (Fig. 17.) The nucleus is black, of a 
Fig. 17. 




105. Solar spots. — Are they constant or variable in number 
and appearance ? How many are sometimes seen on the sun's 
disk at once ? Are they usually large or small 1 How many 
miles in diameter are the largest 1 Describe a spot. What 
changes occur in the nucleus ? What is the umbra ? In what 
part of the sun do the spots mostly appear 1 What apparent 
motions have they ? What is the period of their revolution T 



SOLAR SPOTS. 



73 



very irregular shape, and is subject to great and sudden 
changes, both in form and size. Spots have sometimes 
seemed to burst asunder, and to project fragments in dif- 
ferent directions. The umbra is a wide margin of 
lighter shade, and is often of greater extent than the 
nucleus. The spots are usually confined to a zone ex- 
tending across the central regions of the sun, not exceed- 
ing 60° in breadth. When the spots are observed from 
day to day, they are seen to move across the disk of the 
sun, occupying about two weeks in passing from one 
limb to the other. After an absence of about the same 
period, the spot returns, having taken 27d. 7b. 37m. in 
the entire revolution. 



106. The spots must be nearly 
or quite in contact with the body 
of the sun. Were they at any 
considerable distance from it, the 
time during which they would/ 
be seen on the solar disk, would/ 
be less than that occupied in 
the remainder of the revolution. 
Thus, let S, (Fig. 18,) be the 
sun, E the earth, and abc the path 
of the body, revolving about 
the sun. Unless the spot were 
nearly or quite in contact with 
the body of the sun, being pro- 
jected upon his disk only while 
passing from b to c, and being 
invisible while describing the 
arc cab, it would of course be 
out of sight longer than in sight, 
whereas the two periods are 
found to be equal. Moreover, 



Fig. 18 




106. How are the spots known to be nearly or quite in con- 
tact with the body of the sun 1 Illustrate by figure 18. What 
causes the motion of the spots ? What is the period of the sun's 
revolution on his axis ? Explain by figure 1 9. 

7 



74 



THE SUN. 



the lines which all the solar spots describe on the disk 
of the sun, are found to be parallel to each other, like 
the circles of diurnal revolution around the earth, and 
hence it is inferred that they arise from a similar cause, 
namely, the revolution of the sun on its axis, a fact which 
is thus made known to us. 

But although the spots occupy about 27-|- days in pass- 
ing from one limb of the sun around to the same limb 
again, yet this is not the period of the sun's revolution 
on his axis, but exceeds it by nearly two days. For, 
let AA'B (Fig. 19,) represent the sun, and EE'M the 
orbit of the earth. Thus, when the earth is at E, the 
visible disk of the sun will be 
AA'B ; and if the earth remain- 
ed stationary at E, the time oc- 
cupied by a spot after leaving A 
until it returned to A, would be 
in st equal to the time of the 
sun's revolution on his axis. 
But during the 27^ days in 
which the spot has been per- 
forming its apparent revolution, 
the earth has been advancing 
in his orbit from E to E', where 
the visible disk of the sun is 

A'B'. Consequently, before the spot can appear again 
on the limb from which it set out, it must describe so 
much more than an entire revolution as equals the arc 
AA / , and this occupies nearly two days, which sub- 
tracted from 27-J days, makes the sun's revolution on 
its axis about 25J days ; or more accurately, it is 25d. 
9h. 56m. 




107. A telescope of moderate powers is sufficient to 
show the spots on the sun, and it is earnestly recom- 
mended to the learner to avail himself of the first oppor- 



107. How large a telescope is sufficient to view the spots on 
the sun ? How is the eye protected from the glare of the sun's 
light ? How may these shades be made ? 



SOLAR SPOTS. 75 

tunity he may have, to view them for himself. For ob- 
servations on the sun, telescopes are usually furnished 
with colored glass shades, which are screwed upon the 
end of the instrument to which the eye is applied, foi 
the purpose of protecting the eye from the glare of the 
sun's light. Such screens may be easily made by hold- 
ing a small piece of window glass over the flame of a 
lamp, the wick being raised higher than usual so as to 
smoke freely. 

108. The cause of the solar spots is unknown. It is 
not easy to determine what it is that occasions such 
changes on the surface of the sun ; but various conjec- 
tures have been proposed by different astronomers. Ga- 
lileo supposed that the dark part of a spot is owing to 
black cinders which rise from the interior of the sun, 
where they are formed by the action of heat, constitu- 
ting a kind of volcanic lava that floats upon the surface 
of the fiery flood, which he supposed to constitute the 
outer portion of the sun. But the vast extent which 
these spots occasionally assume is unfavourable to such a 
supposition. It is incredible that a quantity of volcanic 
lava should suddenly rise to the surface of the sun, suffi- 
cient to occupy (as a spot is sometimes found to do) 
2000,000,000 square miles. 

Dr. Herschel proposed a theory respecting the nature 
and constitution of the sun, which, more from respect 
to his authority than on account of any evidence by 
svhich it is supported, has been generally received. Ac- 
cording to him, the sun is itself an opake body like the 
earth, but is enveloped at a considerable distance from 
his body by two different strata of clouds, the exterior 



108. Is the cause of solar spots well known ? What was 
Galileo's hypothesis 1 What objections are there against it \ 
What is Herschel's theory of the nature and constitution of 
the sun ? What sort of a body does he consider the sun itself? 
By what is it encompassed ? Where is the repository of the 
sun's light and heat ? How does he explain the spots ? What 
objections are there to this duwttv ? What are facula? 



78 THE SUN. 

stratum being the fountain from which emanates the 
sun's light and heat. The solar spots arise from the oc- 
casional displacement of portions of this envelope of 
clouds, disclosing to view tracts of the solid body of the 
sun. 

We regard this view of the origin of the sun's light and 
heat as unsubstantiated by any satisfactory proofs, and 
as in itself highly improbable. Such a medium would 
be a very unsuitable repository for the intense heat oi 
the sun, which can arise only from fixed matter in a state 
of high ignition. The most probable supposition is, that 
the surface of the sun consists of melted matter in such 
a state. We must confess our ignorance of any known 
cause which is adequate to explain the sudden extinc- 
tion and removal of so large portions of this fiery flood, 
as is occupied by some of the solar spots. 

Besides the dark spots on the sun, there aie also seen, 
in different parts, places that are brighter than the neigh- 
boring portions of the disk. These are called faculce. 
Other inequalities are observable in powerful telescopes, 
all indicating that the surface of the sun is in a state of 
constant and powerful agitation. 

ZODIACAL LIGHT. 

109. The Zodiacal Light is a faint light resembling 
the tail of a comet, and is seen at certain seasons of the 
year following the course of the sun after evening twi- 
light, or preceding his approach in the morning sky. 
Figure 20 represents its appearance as seen in the even- 
ing in March, 1838. The following are the leading facts 
respecting it. 

1. Its form is that of a luminous pyramid, having its 
base towards the sun. It reaches to an immense dis- 
tance from the sun, sometimes even beyond the orbit of 
the earth. It is brighter in the parts nearer the sun than 
in those that are more remote, and terminates in an ob- 
tuse apex, its light fading away by insensible gradations, 
until it becomes too feeble for distinct vision. Hence 
its limits are at the same time fixed at dhTerent dis- 



ZODIACAL LIGHT. 



77 



Fiff. 23. 




tances from the sun by different observers, according to 
their respective powers of vision. 

2. Its aspects vary very much with the different seasons 
of the year. About the first of October, in our climate 
(Lat. 41° 18') it becomes visible before the dawn of day. 
rising along north of the ecliptic, and terminating above 
the nebula of Cancer. About the middle of November, 
its vertex is in the constellation Leo. At this time no 
traces of it are seen in the west after sunset, but about 
the first of December it becomes faintly visible in the 
west, crossing the Milky Way near the horizon, and 
reaching from the sun to the head of Capricornus, form- 
ing, as its brightness increases, a counterpart to the Milky 



109. Zodiacal Light. — Describe it. When and where 
seen ? What is its form ? How far does it reach ? Where 
brightest ? How do its aspects vary at different seasons of 
the year ? What motions has it ? Is it equally conspicuous 
every year 1 What was it formerly held to be ? W T ith what 
phenomenon has it been supposed to be connected ? 

7* 



78 THE SUN. 

Way, between which on the right, and the Zodiacal 
Light on the left, lies a triangular space embracing the 
Dolphin. Through the month of December, the Zo- 
diacal Light is seen on both sides of the sun, namely, 
before the morning and after the evening twilight, some- 
times extending 50° westward, and 70° eastward of the 
sun at the same time. After it begins to appear in the 
western sky, it increases rapidly from night to night, 
both in length and brightness, and withdraws itself from 
the morning sky, where it is scarcely seen after the 
month of December, until the next October. 

3. The Zodiacal Light moves through the heavens in 
the order of the signs. It moves with unequal velocity, 
being sometimes stationary and sometimes retrogade, 
while at other times it advances much faster than the 
sun. In February and March, it is very conspicuous in 
the west, reaching to the Pleiades and beyond ; but in 
April it becomes more faint, and nearly or quite disap- 
pears during the month of May. It is scarcely seen in 
this latitude during the summer months. 

4. It is remarkably conspicuous at certain periods of 
a few years, and then for a long interval almost disap- 
pears. 

5. The Zodiacal Light was formerly held to be the 
atmosphere of the sun. But La Place has shown that 
the solar atmosphere could never reach so far from the 
sun as this light is seen to extend. It has been supposed 
by others to be a nebulous body revolving around the 
sun. The author of this work has ventured to suggest 
the idea, that the extraordinary Meteoric Showers, which 
at different periods visit the earth, especially in the 
month of November, may be derived from this body. 
See American Journal of Science, Vol. 29, p. 378. 



79 



CHAPTER II. 



OF THE APPARENT ANNUAL MOTION OF THE SUN- 
FIGURE OF THE EARTH'S ORBIT. 



-SEASONS 



110. The revolution of the earth around the sun once 
a year, produces an apparent motion of the sun around 
the earth in the same period. When bodies are at such 
a distance from each other as the earth and the sun, a 
spectator on either would project the other body upon 
the concave sphere of the heavens, always seeing it on 
the opposite side of a great circle, 180° from himself. 
Thus when the earth arrives at Libra (Fig. 21,) we see 

Fig. 21. 




the sun in the opposite sign Aries. When the earth 
moves from Libra to Scorpio, as we are unconscious of 
our own motion, the sun it is that appears to move from 
Aries to Taurus, being always seen in the heavens, where 



80 THE SUN. 

a line drawn from the eye of the spectator through the 
body meets the concave sphere of the heavens. Hence 
the line of projection carries the sun forward on one 
side of the ecliptic, at the same rate as the earth moves 
on the opposite side ; and therefore, although we are un- 
conscious of our own motion, we can read it from day to 
day in the motions of the sun. If we could see the stars 
at the same time with the sun, we could actually observe 
from day to day the sun's progress through them, as we 
observe the progress of the moon at night ; only the 
sun's rate of motion would be nearly fourteen times 
slower than that of the moon. Although we do not see 
the stars when the sun is present, yet after the sun is set, 
we can observe that it makes daily progress eastward, 
as is apparent from the constellations of the Zodiac oc- 
cupying, successively, the western sky after sunset, pro- 
ving that either all the stars have a common motion east- 
ward independent of their diurnal motion, or that the 
sun has a motion past them, from west to east. We 
shall see hereafter abundant evidence to prove, that this 
change in the relative position of the sun and stars, is 
owing to a change in the apparent place of the sun, 
and not to any change in the stars. 

111. Although the apparent revolution of the sun is 
in a direction opposite to the real motion of the earth, as 
regards absolute space, yet both are nevertheless from 
west to east, since these terms do not refer to any direc- 
tions in absolute space, but to the order in which certain 
constellations (the constellations of the Zodiac) succeed 
one another. The earth itself, on opposite sides of its 
orbit, does in fact move towards directly opposits points 



110. What produces the apparent motion of the sun around 
the earth once a year ? How would a spectator on either body 
see the other 1 When the earth is at Libra, where does the 
sun appear to be 1 Explain figure 21. If the stars were visi- 
ble in the day time, how could we determine the sun's path ? 
What change do the constellations of the Zodiac undergo with 
respect to the sun ? 



ANNUAL MOTION. 81 

of space ; but it is all the while pursuing its course in 
the order of the signs. In the same manner, although 
the earth turns on its axis from west to east, yet any 
place on the surface of the earth is moving in a direc- 
tion in space exactly opposite to its direction twelve 
hours before. If the sun left a visible trace on the face 
of the sky, the ecliptic would of course be distinctly 
marked on the celestial sphere as it is on an artificial 
globe ; and were the equator delineated in a similar man- 
ner, (by any method like that supposed in Art. 33,) we 
should then see at a glance the relative position of these - 
two circles, the points where they intersect one another 
constituting the equinoxes, the points where they are at 
the greatest distance asunder, or the solstices, and vari- 
ous other particulars, which for want of such visible 
traces, we are now obliged to search for by indirect and 
circuitous methods. It will even aid the learner to have 
constantly before his mental vision, an imaginary delin- 
eation of these two important circles on the face of the 
sky. 

112. The equator makes an angle with the ecliptic of 
23° 28'. This is called the obliquity of the ecliptic. 
As the sun and earth are both always in the ecliptic, and 
as the motion of the earth in one part of it makes the 
sun appear to move in the opposite part at the same rate, 
the sun apparently descends in the winter 23° 28' to the 
south of the equator, and ascends in the summer the 
same number of degrees to the north of it. We must 
keep in mind that the celestial equator and the celestial 
ecliptic are here understood, and we may imagine them 



111. In what sense are the motions of the sun and earth 
opposite, and in what sense in the same direction 1 If the 
ecliptic and equator were distinctly delineated on the face of 
the sky, what points in them could be easily observed 1 

112. What angle does the equator make with the ecliptic? 
In what circle do the sun and earth always appear ? How far 
do they recede from the equator ? How does the obliquity of 
the ecliptic vary ! 



82 THE SUN. 

to be two great circles distinctly delineated on the face 
of the sky. On comparing observations made at differ- 
ent periods for more than two thousand years, it is found, 
that the obliquity of the ecliptic is not constant, but 
that it undergoes a slight diminution from age to age, 
amounting to 52" in a century, or about half a second 
annually. We might apprehend that by successive ap- 
proaches to each other the equator and ecliptic would 
finally coincide ; but astronomers have found by a most 
profound investigation, founded on the principles of 
universal gravitation, that this variation is confined with- 
in certain narrow limits, and that the obliquity, after di- 
minishing for some thousands of years, will then in- 
crease for a similar period, and will thus vibrate for ever 
about a mean value. 

113. Let us conceive of the sun as at that point of the 
ecliptic where it crosses the equator, that is, at one of the 
equinoxes, as the vernal equinox. Suppose he stands 
still then for twenty four hours. The revolution of the 
earth on its axis from east to west during this twenty 
four hours, will make the sun appear to describe a great 
circle from east to west, coinciding with the equator. 
At the end of this period, suppose the sun to move 
northward one degree and to remain there for the next 
twenty-four hours, in which time the revolution of the 
earth will make the sun appear to describe another cir- 
cle from east to west, parallel to the equator, but one 
degree north of it. Thus we may conceive of the sun 
as moving one degree every day for about three months, 
when it will reach the point of the ecliptic farthest 
from the equator, which is called the tropic from a Greek 



113. Suppose the sun to start from the equator and to ad- 
vance one degree north daily, explain its apparent diurnal rev- 
olutions. When is the sun at the northern tropic ? When is 
he at the southern tropic ? How are the respective meridian 
altitudes of the sun at these periods ? How do we find from 
these observations, the obliquity of the ecliptic ? 



THE SEASONS. 



66 



word (igsnco) which signifies to turn, because when the 
sun arrives at this point, his motion in his orbit carries 
him continually towards the equator, and therefore he 
seems to turn about. 

When the sun is at the northern tropic, which hap- 
pens about the 21st of June, his elevation above the 
southern horizon at noon, is the greatest of the year ; 
and when he is at the southern tropic, about the 21st 
of December, his elevation at noon is the least in the 
year. The difference between these two meridian alti- 
tudes, will give the whole distance from one tropic to 
the other, and consequently twice the distance from each 
tropic to the equator. By this means we find how far 
the tropic is from the equator, and that gives us the in- 
clination of the two circles to one another ; for the great- 
est distance between any two great circles on the sphere, 
is always equal to the angle which they make with each 
other. 



114. The dimensions of the earth's orbit, when com- 
pared with its own magnitude, are immense. 

Since the distance of the earth from the sun is 
95,000,000 miles, and the length of the entire orbit nearly 
600,000,000 miles, it will be found, on calculation, that 
the earth moves 1,640,000 miles per day, 68,000 miles 
per hour, 1,100 miles per minute, and nearly 19 miles 
every second, a velocity nearly sixty times as great as 
the maximum velocity of a cannon ball. A place on 
the earth's equator turns, in the diurnal revolution, at the 
rate of about 1,000 miles an hour and ^ of a mile per 
second. The motion around the sun, therefore, is nearly 
seventy times as swift as the greatest motion around the 
axis. 



114. What is said of the dimensions of the earth's orbit ? 
At what rate does the earth move in its orbit per day, hour, 
minute, and second 1 How far does a place on the earth's 
equator move per hour and second ? How much swifter is 
the motion in the orbit than on its axis ? 



84 THE SUN. 

THE SEASONS. 

115. The change of seasons depends on two causes, 
(1) the obliquity of the ecliptic, and (2) the earth's axis 
always remaining parallel to itself Had the earth's 
axis been perpendicular to the plane of its orbit, the 
equator would have coincided with the ecliptic, and the 
sun would have constantly appeared in the equator 
To the inhabitants of the equatorial regions, the sun 
would always have appeared to move in the prime ver- 
tical ; and to the inhabitants of either pole, he would 
always have been in the horizon. But the axis being 
turned out of a perpendicular direction 23° 28', the 
equator is turned the same distance out of the ecliptic ; 
and since the equator and ecliptic are two great circles 
which cut each other in two opposite points, the sun, 
while performing his circuit in the ecliptic, must evi- 
dently be once a year in each of those points, and must 
depart from the equator of the heavens to a distance on 
either side equal to the inclination of the two circles, 
that is, 23° 28'. 

116. The earth being a globe, the sun constantly en- 
lightens the half next to him,* while the other half is in 
darkness. The boundary between the enlightened and 
unenlightened part, is called the circle of illumination. 
When the earth is at one of the equinoxes, the sun is at 
the other, and the circle of illumination passes through 
both the Doles. When the earth reaches one of the 



115. The Seasons. — On what two causes does the change 
of seasons depend 1 Had the earth's axis been perpendicu- 
lar to the plane of its orbit, in what great circle would the sun 
always have appeared to move 1 



* In fact, the sun enlightens a little more than half the earth, since 
on account of his vast magnitude the tangents drawn from opposite 
sides of the sun to opposite sides of the earth, converge to a point 
behind the earth, as will be seen by and by in the representation of 
eclipses 



THE SEASONS. 



85 



tropics, the sun being at the other, the circle of illumin- 
ation cuts the earth, so as to pass 23° 28' beyond the 
nearer, and the same distance short of the remoter pole. 
These results would not be uniform, were not the earth's 
axis always to remain parallel to itself. The following 
figure will illustrate the foregoing statements. 
Fig. 22. 




Let ABCD represent the earth's place in different 
parts of its orbit, having the sun in the center. Let A, 



116. How much of the earth does the sun enlighten at once ? 
Define the circle of illumination. How does it cut the earth at 
the equinoxes ? How at the solstices 1 Explain figure 22. 
When the earth is at one of the tropics and the sun at the 
other, where is it continual day and where continual night ? 

8 



86 THE SUN. 

C, be the positions of the earth at the equinoxes, and B, 

D, its positions at the tropics, the axis ns being always 
parallel to itself.* At A and C the sun shines on both 
n and s ; and now let the globe be turned round on its 
axis, and the learner will easily conceive that the sun 
will appear to describe the equator, which being bisected 
by the horizon of every place, of course the day and 
night will be equal in all parts of the globe. f Again, 
at B when the earth is at the southern tropic, the sun 
shines 23J° beyond the north pole n, and falls the same 
distance short of the south pole s. The case is exactly 
reversed when the earth is at the northern tropic and 
the sun at the southern. While the earth is at one of 
the tropics, at B for example, let us conceive of it as turn- 
ing on its axis, and we shall readily see that all that part 
of the earth which lies within the north polar circle will 
e-njoy continual day, while that within the south polar 
circle will have continual night, and that all other places 
will have their days longer as they are nearer to the en- 
lightened pole, and shorter as they are nearer to the un- 
enlightened pole. This figure likewise shows the suc- 
cessive positions of the earth at different periods of the 
year, with respect to the signs, and what months corres- 
pond to particular signs. Thus the earth enters Libra 
and the sun Aries on the 21st of March, and on the 21st 
of June the earth is just entering Capricorn and the sun 
Cancer. 

117. Had the axis of the earth been perpendicular 
to the plane of the ecliptic, then the sun would always 
have appeared to move in the equator, the days would 
every where have been equal to the nights, and there 
could have been no change of seasons. On the other 
hand, had the inclination of the ecliptic to the equator 



* The learner will remark that the hemisphere towards n is above, 
and that towards 5 is below the plane of the paper. It is important to 
form a just conception of the position of the axis with respect to the 
plane of its orbit. 

t At the pole, the solar disk, at the time of the equinox, appears bis- 
ected by the horizon. 



THE SEASONS. 87 

been much greater than it is, the vicissitudes of the sea- 
sons would have been proportionally greater than at pres- 
ent. Suppose, for instance, the equator had been at 
right angles to the ecliptic, in which case the poles of 
the earth would have been situated in the ecliptic itself; 
then in different parts of the earth the appearances 
would have been as follows. To a spectator on the 
equator, the sun as he left the vernal equinox would 
every day perform his diurnal revolution in a smaller 
and smaller circle, until he reached the north pole, when 
he would halt for a moment, and then wheel about and 
return to the equator in the reverse order. The pro- 
gress of the sun through the southern signs, to the south 
pole, would be similar to that already described. Such 
would be the appearances to an inhabitant of the equa- 
torial regions. To a spectator living in an oblique 
sphere, in our own latitude for example, the sun while 
north of the equator would advance continually north- 
ward, making his diurnal circuits in parallels farther and 
farther distant from the equator, until he reached the 
circle of perpetual apparition, after which he would 
climb by a spiral course to the north star, and then as 
rapidly return to the equator. By a similar progress 
southward, the sun would at length pass the circle of 
perpetual occultation, and for some time (which would 
be longer or shorter according to the latitude of the place 
of observation) there would be continual night. 

The great vicissitudes of heat and cold which would 
attend such a motion of the sun, would be wholly in- 
compatible with the existence of either the animal or 
the vegetable kingdoms, and all terrestrial nature would 



117. Had the earth's axis been perpendicular to the plane 
of the ecliptic, would there have been any change of seasons ? 
What would have been the consequence had the equator been 
at right angles to the ecliptic ? How would the sun appear to 
move to a person on the equator ? How to one situated at the 
pole 1 How to an inhabitant of an oblique sphere ? How 
would have been the vicissitudes of heat and cold ? 



88 



THE SUN. 



be doomed to perpetual sterility and desolation. The 
happy provision which the Creator has made against 
such extreme vicissitudes, by confining the changes of 
the seasons within such narrow bounds, conspires with 
many other express arrangements in the economy of 
nature to secure the safety and comfort of the human 



race. 



FIGURE OF THE EARTHS ORBIT. 

118. Thus far we have taken the earth's orbit as a 
great circle, such being the projection of it on the celes- 
tial sphere ; but we now proceed to investigate its actual 
figure. 



Fig. 23. 




Were the earth's path a circle, having the sun in the 
center, the sun would always appear to be at the same 



118. Were the earth's path a circle, how would the distance 
of the sun from us always appear ? Define the radius vector. 
What do we infer from the fact that the radius vector is con- 
stantly varying ? How do we learn the relative distances ot 
the earth ? How do we construct a figure representing the 
earth's orbit ? Explain figure 23. 



FTGURE OF THL EARTH'S ORBIT. 89 

distance from us ; that is, the radius of its orbit, or ra- 
dius vector, the name given to a line drawn from the 
center of the sun to the orbit of any planet, would al- 
ways be of the same length. But the earth's distance 
from the sun is constantly varying, which shows that 
its orbit is not a circle. We learn the true figure of the 
orbit, by ascertaining the relative distances of the earth 
from the sun at various periods of the year. These all 
being laid down in a diagram, according to their respec- 
tive lengths, the extremities, on being connected, give 
us our first idea of the shape of the orbit, which appears 
of an oval form, and at least resembles an ellipse ; and, 
on further trial, we find that it has the properties of an 
ellipse. Thus, let E (Fig. 23,) be the place of the 
earth, and a, b, c, &c. successive positions of the sun ; 
the relative lengths of the lines E#, Eft, &c. being 
known : on connecting the points, a, b, c, &c. the result- 
ing figure indicates the true shape of the earth's orbit. 

119. These relative distances are found in two differ- 
ent ways ; first, by changes in the sun's apparent diam- 
eter, and, secondly, by variations in his angular velo- 
city. The same object appears to us smaller in propor- 
tion as it is more distant ; and if we see a heavenly body 
varying in size at different times, we infer that it is at 
different distances from us ; that when largest, it is near- 
est to us, and when smallest, farthest off. Now when 
the sun's diameter is measured accurately by instru- 
ments, it is found to vary from day to day, being when 
greatest more than thirty-two minutes and a half, and 
when smallest only thirty-one minutes and a half, differ- 
ing in all, about seventy-five seconds. When the diam- 
eter is greatest, which happens in January, we know 



119. How does the same body appear when at different dis- 
tances 1 What inferences do we make from its variations of 
size ? How much does the apparent diameter of the snn vary 
in different parts of the year ? When is it greatest, and 
when smallest ? Define the terms perihelion and aphelion. 

8* 



90 THE SUN 

that the sun is nearest to us ; and when the diameter is 
least, which occurs in July, we infer that the sun is at 
the greatest distance from us. 

The point where the earth or any planet, in its revo- 
lution, is nearest the sun, is called its perihelion ; the 
point where it is farthest from the sun, its aphelion, 

120. Similar conclusions may be drawn from obser- 
vations on the sun's angular velocity. A body appears 
to move most rapidly when nearest to us. Indeed the 
apparent velocity of the sun increases rapidly as it ap- 
proaches us, and as rapidly diminishes when it recedes 
from us. If it were to come twice as near as before it 
would appear, to move not merely twice as swift, but 
four times as swift ; if it came ten times nearer, its appa- 
rent velocity would be one hundred times as great as 
before. We say, therefore, that the velocity varies 
inversely as the square of the distance, for as the dis- 
tance is diminished ten times, the velocity is increased 
the square of ten, that is, one hundred times. Now by 
noting the time it takes the sun, from day to day, to re- 
turn to the meridian, we learn the comparative veloci- 
ties with which it moves at different times, and from 
these we derive the comparative distances of the sun 
at the corresponding times. 

When by either of the foregoing methods, we have 
learned the relative distances of the sun from the earth 
at various periods of the year, we may lay down, or plot 
in a diagram like figure 23, a representation of the orbit 
which the sun apparently describes about the earth, and 
it will give us the figure of the orbit which the earth 
really describes about the sun, in its annual revolution. 



120. What conclusions are drawn from the variations in 
the sun's angular velocity 1 According to what law does the 
velocity vary ? How may we ascertain the sun's daily rate ? 
What great doctrine is it necessary to be acquainted with, in 
order to understand the celestial motions ? 



UNIVERSAL GRAVITATION. 91 

But neither the revolution of the earth about the sun, 
nor indeed that of any of the planets, can be well and 
clearly understood, until we are acquainted with the 
forces by which their motions are produced, especially 
with the doctrine of Universal Gravitation. To this 
subject, therefore, let us next apply our attention. 



CHAPTER III. 

OF UNIVERSAL GRAVITATION KEPLER'S LAWS MOTION 

IN AN ELLIPTICAL ORBIT PRECESSION OF THE EQUI- 
NOXES. 

121. We discover in nature a tendency of every por- 
tion of matter towards every other. This tendency is 
called gravitation. In obedience to this power, a stone 
falls to the ground and a planet revolves around the sun. 

It was once supposed that we could not reason from 
the phenomena of the earth to those of the heavens ; 
since it was held that the laws of motion might be 
very different among the heavenly bodies from what 
we find them to be on this globe ; but Galileo and New- 
ton in their researches into nature, proceeded on the 
idea that nature is uniform in all her works, and that 
every where the same causes produces the same effects, 
and that the same effects result from the same causes. 
That this is a sound principle of philosophy, is proved 
by the fact, that all the conclusions derived from it in 
the interpretation of nature are found to be true. Hence 
by studying the laws of motion as exhibited constantly 
before our eyes in all terrestrial motions, we are learning 



121. What force do we observe in nature ? What is this 
force called ? Can we reason from terrestrial to celestial phe- 
nomena ? On what idea did Galileo and Newton proceed ? 
How is this proved to be a sound principle of philosophy I 



92 UNIVERSAL GRAVITATION". 

the laws that govern the movements of the heavenly 
bodies. 

122. On the earth all bodies are seen to fall towards 
its center. A stone let fall in any part of the earth, de- 
scends immediately to the ground. This may seem to 
the young learner as so much a matter of course as to 
require no explanation. But stones fall in exactly op- 
posite directions on opposite sides of the earth, always 
falling towards the center of the earth from every part 
exterior to its surface ; as when Fl S- 24 - 

we hold a small needle towards n^ ^dliillllSIIIlillllfiiilliiiiKy^' 
a magnetic ball or load stone, the 
needle will fly towards the ball, 
and cling to its surface, to which- 
ever side of the ball it is present- 
ed. (Fig. 24.) From this uni- 
versal descent of bodies near the y* 
earth, we infer the existence of ' 
some force which draws or impels them, and this invisi- 
ble force we call the attraction of gravitation, or simply 
gravity. 

123. By the laws of gravity we mean the manner in 
which it always acts. They are three in number, and 
are comprehended in the following proposition : 

Gravity acts on all matter alike, with a force propor- 
tioned to the quantity of matter, and inversely as the 
square of the distance. 

First, gravity acts on all matter alike. Every body 
in nature, whether great or small, whether solid, liquid, 
or aeriform, exhibits the same tendency to fall towards 
the center of the earth. Some bodies, indeed, seem less 
prone to fall than others, and some even appear to rise, 
as smoke and light vapors. But this is because they are 
supported by the air ; when that is removed, they de- 




122. In what directions do bodies fall in all parts of the 
earth ? Illustrate by figure 24. What is gravity ? 



LAWS OF GRAVITY. 



93 



scend alike towards the earth ; a guinea and a feather, 
the lightest vapor and the heaviest rocks, fall with equal 
velocities. 

Secondly, the force of gravity is proportioned to the 
quantity of matter. A mass of lead contains perhaps 
fifty times as much matter as an equal bulk of cotton ; 
yet, if carried beyond the atmosphere, and let fall in ab- 
solute space, they would both descend towards the earth 
with equal speed, until they entered the atmosphere, 
and were the atmosphere removed they would continue 
to fall side by side until they reached the earth. Now 
if the lead contains fifty times as much matter as the 
cotton, it must take fifty times the force to make it move 
with equal velocity. If we double the load we must 
double the team, if we would continue to travel at the 
same speed as before. Hence, from the fact that bodies 
of various degrees of density descend alike towards the 
center of the earth by the force of gravity, we infer 
that that force is always exerted upon bodies in exact 
proportion to their quantity of matter. 

Thirdly, the force with which gravity acts upon bod- 
ies at different distances from the earth, is inversely as 
the square of the distance from the center of the earth. 
If a pound of lead were carried as far above the earth as 
from the center to the surface of the earth, it would 
weigh only one-fourth of a pound ; for being twice as 
far as before from the center of the earth, its weight 
would be diminished in the proportion of the square of 
two, that is, four times. 



123. What do we mean by the law of gravity 1 State the 
general proposition. Show that gravity acts on all matter alike 
How is this consistent with the fact, that some bodies appear to 
rise ? How would all bodies fall in a vacuum 1 Explain how 
gravity is proportioned to the quantity of matter. How would 
equal masses of lead and cotton fall, if carried beyond the at- 
mosphere 1 What do we infer from the fact, that all bodies fall 
towards the earth with equal velocities ? To what is gravity 
acting at different distances proportioned ? How much would 
a pound of lead weigh, if carried as far above the earth as from 
v .he surface to the center ? 



94 UNIVERSAL GRAVITATION. 

124. Bodies falling to the earth by gravity have their 
velocity continually increased. For since they retain 
what motion they have and constantly receive more 
by the continued action of gravity, they must move 
faster and faster, as a wheel has its velocity constantly 
accelerated when we continue to apply successive im- 
pulses to it. 

The spaces which bodies describe, when falling freely 
by gravity, are as the squares of the times. It is found 
by experiment, that a body will fall from a state of 
rest 16 j2 feet in one second. In two seconds it will not 
fall merely through double this space, but through four 
times this space, that is, through a distance expressed 
by the square of the time multiplied into ISy^- Conse- 
quently, in two seconds the fall will be 64J, in three se- 
conds 144J, and in ten seconds 1608J feet, that is, 
through one hundred times 16^2 feet. 

The weight of a body is nothing more than the ac- 
tion of gravity upon it tending to carry it towards the 
center of the earth. The counterpoise which is placed 
in the opposite scale by which its weight is estimated, is 
the force it takes to hold the body back, which must be 
just equal to that by which it endeavors to descend. 

125. There is another principle which it is necessary 
clearly to comprehend before we can understand the mo- 
tions of the heavenly bodies. It is commonly called the 
First Law of Motion and is as follows : 

Every body perseveres in a state of rest, or of uniform 
motion in a straight line, unless compelled by some force 
to change its state. This law has been fully established 
by experiment, and is conformable to all experience. 
It embraces several particulars. First, A body when at 



124. When a body is falling towards the earth, how is its 
velocity affected ? To what are the spaces described by fall- 
ing bodies proportioned ? How far will a body fall from a state 
of rest in one second 1 How far in two seconds ? What is 
the weight of a body ? 



LAWS OF MOTION. 95 

rest remains so unless some force puts it in motion ; 
and hence it is inferred, when a body is found in mo- 
tion, that some force must have been applied to it suffi- 
cient to have caused its motion. Thus, the fact that 
the earth is in motion around the sun and around its own 
axis, is to be accounted for by assigning to each of these 
motions a force adequate, both in quantity and direction, 
to produce these motions respectively. 

Secondly, When a body is once in motion it will con- 
tinue to move forever, unless something stops it. When 
a ball is struck on the surface of the earth, the friction 
of the earth and the resistance of the air soon stop its 
motion ; when struck on smooth ice it will go much 
farther before it comes to a state of rest, because the ice 
opposes much less resistance than the ground ; and were 
there no impediment to its motion it would, when once 
set in motion, continue to move without end. The 
heavenly bodies are actually in this condition : they 
continue to move, not because any new forces are ap- 
plied to them, but, having been once set in motion, they 
continue in motion because there is nothing to stop them. 

Thirdly, The motion to which a body naturally tends 
is uniform ; that is, the body moves just as far the se- 
cond minute as it did the first, and as far the third as 
the second, passing over equal spaces in equal times. 

Fourthly, A body in motion will move in a straight 
line, unless diverted out of that line by some external 
force ; and the body will resume its straight forward mo- 
tion, when ever the force that turns it aside is with- 
drawn. Every body that is revolving in an orbit, like 
the moon around the earth, or the earth around the sun, 



125. Recite the first law of motion. How has this law been 
established ? What does the fact, that the earth is in motion 
around the sun imply? How would a ball when once struck 
continue to move, if it met with no resistance ? Why do the 
heavenly bodies continue to move ? What is meant by saying 
that motion is naturally uniform ? In what direction does 
every revolving bodv tend to move. 



96 UNIVERSAL GRAVITATION. 

tends to move in a straight line which is a tangent* to 
its orbit. 

Let us now see how the foregoing principles, which 
operate upon bodies on the earth, are extended so as to 
embrace all bodies in the universe, as in the doctrine of 
Universal Gravitation. This important principle is thus 
defined : 

126. Universal gravitation, is that influence by 
which every body in the universe, whether great or small, 
tends towards every other, with a force which is directly 
as the quantity of matter, and inversely as the square of 
the distance. 

As this force acts as though bodies were drawn to- 
wards each other by a mutual attraction, the force is de- 
nominated attraction; but it must be borne in mind, 
that this term is figurative, and implies nothing respect- 
ing the nature of the force. 

The existence of such a force in nature was distinctly 
asserted by several astronomers previous to the time of 
Sir Isaac Newton, but its laws were first promulgated 
by this wonderful man in his Principia, in the year 1687. 
It is related, that while sitting in a garden, and musing 
on the cause of the falling of an apple, he reasoned 
thus :f that, since bodies far removed from the earth fall 
towards it, as from the tops of towers, and the highest 
mountains, why may not the same influence extend 
even to the moon ; and if so, may not this be the reason 
why the moon is made to revolve around the earth, as 
would be the case with a cannon ball were it projected 
horizontally near the earth with a certain velocity. Ac- 
cording to the first law of motion, the moon, if not con- 
tinually drawn or impelled towards the earth by some 
force, would not revolve around it, but would proceed 
on in a straight line. But going around the earth as she 
does, in an orbit that is nearly circular, she must be 



* A tangent is a straight line which touches a curve. Thus AB (Fig. 
25,) is a tangent to the circle at«A. 

t Pemberton's View of Newton's Philosophy. 



UNIVERSAL KRAVITATION. 



97 



urged towards the earth by some force, which diverts 
her from a straight course. For let the earth (Fig. 25.) 
be at E, and let the arc described by the moon in one 
second of time be Ab. Were the moon influenced by 
no extraneous force, to turn aside, she would have de- 
scribed, not the arc Ab, but the straight line AB, and 
would have been found at the end of the given time at 
B instead of b. She therefore departs from the line in 
which she tends naturally to move, by the line B&, 
which in small angles may be taken as equal to Aa. 
Fig. 25. 




This deviation from the tangent must be owing to some 
extraneous force. Does this force correspond to what 
the force of gravity exerted by the earth, would be at 
the distance of the moon ? The question resolves itself 
into this : Would the force of gravity exerted by the 
earth upon the moon, cause the moon to deviate from 
her straight forward course towards the earth just as 
much as she is actually found to deviate ? Now we 



126. Universal Gravitation. — Define it. Why called at- 
traction ? State the historical facts connected with its discov- 
ery. How did Sir Isaac Newton reason from the falling of an 
apple ? Explain by figure 25. How is it proved that gravity 
and no other force causes the moon to revolve about the earth ? 

9 



98 UNIVERSAL GRAVITATION. 

know how far the moon is from the earth, namely ; sixty 
times as far as it is from the center to the surface of the 
earth ; and since the force of gravity decreases in pro- 
portion to the square of the distance, this force must be 
3600 times (which equals the square of 60,) less than at 
the surface of the earth. This is found, on computa- 
tion, to be exactly the force required to make the moon 
deviate to the amount she does from the straight line in 
which she constantly tends to move ; and hence it is 
inferred that gravity, and no other force than gravity, 
causes the moon to circulate around the earth. 

By this process it was discovered that the law of grav- 
itation extends to the moon. By subsequent inquiries 
it was found to extend in like manner to all the planets, 
and to every member of the solar system ; and, finally, 
recent investigations have shown that it extends to the 
fixed stars. The law of gravitation, therefore, is now 
established as the grand principle which governs all the 
motions of the heavenly bodies. 



127. There are three great principles, according to 
which the motions of the earth and all the planets 
around the sun are regulated, called Kepler's Laws, hav- 
ing been first discovered by the great astronomer whose 
name they bear. They may appear to the young learner, 
when he first reads them, dry and obscure ; yet they 
will be easily understood from the explanations that fol- 
low ; and so important have they proved in astronomical 
inquiries, that they have acquired for their renowned 
discoverer the exalted appellation of the legislator of the 
skies. 

We will consider each of these laws separately. 



127. Kepler's Laws. — Why so called ? What appellation 
has been given to Kepler ? 



KEPLER'S LAWS. 



99 



128. First law. The orbits of the earth and all the 
planets are ellipses, having the sun in the common 
focus. 

In a circle all the diameters are equal to each other ; 
but if we take a metallic wire or hoop and draw it out on 
opposite sides, we elongate it into an ellipse, of which the 
different diameters are very unequal. That which con- 
nects the two points most distant from each other is called 
the transverse, and that which is at right angles to this 
is called the conjugate axis. Thus AB (Fig. 26) is the 




transverse axis and CD the conjugate of the ellipse AB. 
By such a process of elongating the circle into an el- 
lipse, the center of the circle may be conceived of as 
drawn opposite ways to E and F, each of which be- 
comes a focus, and both together are called the foci of the 
ellipse. The distance GE or GF of the focus from the 



128. Recite the first law. In a circle, how are all the diam- 
eters ? How are. they in an ellipse ? What is the longest di- 
ameter called 1 What is the shortest called ? Explain by figure 
26. What is the eccentricity of the ellipse ? How many el- 
lipses may there be having a common focus 1 Explain figure 
26 How eccentric is the earth's orbit ? 



100 



UNIVERSAL GRAVITATION. 



center is called the eccentricity of the ellipse ; and the 
ellipse is said to be more or less eccentric, as the distance 
of the focus from the center is greater or less. 

Now there may be an indefinite number of ellipses 
having one common focus, but varying greatly in ec- 
centricity. Figure 27 represents such a collection of 




ellipses around the common focus F, the innermost AGD 
having a small eccentricity or varying little from a cir- 
cle, while the outermost ACB is a very eccentric ellipse. 
The orbits of all the bodies that revolve about the sun, 
both planets and comets, have, in like manner, a com- 
mon focus in which the sun is situated, but they differ 
in eccentricity. 

Most of the planets have orbits of very little eccen- 
tricity, differing little from circles, but comets move in 
very eccentric ellipses. 

The earth's path around the sun varies so little from 
a circle, that a diagram representing it truly would 
scarcely be distinguished from a perfect circle ; yet 
when the comparative distances of the sun from the 
earth are taken at different seasons of the year, as is ex- 
plained in Art. 118, we find that the difference between 



kepler's laws. 101 

the greatest and least distances is no less than 3,000,000 

miles. 

129. Second law. The radius vector of the earth, 
or of any planet, describes equal areas in equal times. 

It will be recollected that the radius vector is a line 
drawn from the center of the sun to a planet revolving 
about the sun, (Art. 118.) Thus Ea, Eb, Ec, (Fig. 23,) 
&c. are successive representations of the radius vector. 
Now if a planet sets out from a and travels round the sun 
in the direction of abc, it will move faster when nearer the 
sun, as at a, than when more remote from it, as at m ; 
yet if ab and mn be arcs described in equal times, then, 
according to the foregoing law, the space Eab will be 
equal to the space Emn ; and the same is true of all the 
other spaces described in equal times. Although the 
figure Eab is much shorter than Emn, yet its greater 
breadth exactly counterbalances the greater length of 
those figures which are described by the radius vector 
where it is longer. 

i30. Third law. The squares of the periodical times 
are as the cubes of the mean distances from the sun. 

The periodical time of a body is the time it takes to 
complete its orbit in its revolution about the sun. Thus 
the earth's periodic time is one year, and that of the 
planet Jupiter is about twelve years. As Jupiter takes 
so much longer time to travel round the sun than the 
earth does, we might suspect that his orbit was larger 
than that of the earth, and of course that he was at 
a greater distance from the sun, and our first thought 
might be that he was probably twelve times as far off; 
but Kepler discovered that the distances did not increase 
as fast as the times increased, but that the planets which 



129. State Kepler's second law. Explain by figure 23, p. 88. 

130. State Kepler's third law. What is meant by the peri- 
odical time of a body ? Do planets move faster or slower as 
they are more distant from the sun ? Explain the law. 

9* 



102 UNIVERSAL GRAVITATION. 

are more distant from the sun actually move slower than 
those which are nearer. After trying a great many pro- 
portions, he at length found that if we take the squares 
of the periodic times of two planets, the greater square 
contains the less, just as often as the cube of the dis- 
tance of the greater contains that of the less. This fact 
is expressed by saying, that the squares of the periodic 
times are to one another as the cubes of the distances. 
This law is of great use in determining the distances 
of all the planets from the sun, as we shall see more fully 
hereafter. 

MOTION IN AN ELLIPTICAL ORBIT. 

131. Let us now endeavor to gain a just conception 
of the forces by which the earth and all the planets are 
made to revolve about the sun. 

In obedience to the first law of motion, every moving 
body tends to move in a straight line ; and were not the 
planets deflected continually towards the sun by the 
force of attraction, these bodies as well as others would 
move forward in a rectilineal direction. We call the force 
by which they tend to such a direction the projectile 
force, because its effects are the same as though the body 
were originally projected from a certain point in a certain 
direction. It is an interesting problem for mechanics to 
solve, what was the nature of the impulse originally 
given to the earth, in order to impress upon it its two 
motions, the one around its own axis, the other around 
the sun. If struck in the direction of its center of 
gravity it might receive a forward motion, but no rota- 
tion on its axis. It must, therefore, have been impelled 
by a force, whose direction did not pass through its 



131. Explain how a body is made to revolve in an orbit, 
under the action of two forces. What is meant by the projec- 
tile force ? How must the earth have been impelled in order 
to receive its present motions ? How illustrated by the mo- 
tions of a top 1 



MOTION IN AN ELLIPTICAL ORBIT. 103 

center of gravity. Bernouilli, a celebrated mathemati- 
cian, has calculated that the impulse must have been 
given very nearly in the direction of the center, the 
point of projection being only the 165th part of the 
earth's radius from the center. This impulse alone 
would cause the earth to move in a right line : gravita- 
tion towards the sun causes it to describe an orbit. 
Thus a top spinning on a smooth plane, as that of glass 
or ice, impelled in a direction not coinciding with that 
of the center of gravity, may be made to imitate the two 
motions of the earth, especially if the experiment is tried 
in a concave surface like that of a large bowl. The re- 
sistance occasioned by the surface on which the top 
moves, and that of the air, will gradually destroy the 
force of projection and cause the top to revolve in a 
smaller and smaller orbit ; but the earth meets with no 
such resistance, and therefore makes both her days and 
years of the same length from age to age. A body, 
therefore, revolving in an orbit about a center of attrac- 
tion, is constantly under the influence of two forces, — 
the projectile force, which tends to carry it forward in a 
straight line which is a tangent to its orbit, and the cen- 
tripetal force, by which it tends towards the center. 

132. At an example of a body revolving in an orbit 
under the influence of two forces, suppose a body pla- 
ced at any point P (Fig. 28,) above the surface of the 
earth, and let PA be the direction of the earth's center. 
If the body were allowed to move without receiving 
any impulse, it would descend to the earth in the direc- 
tion PA with an accelerated motion. But suppose that 
at the moment of its departure from P, it receives an 
impulse in the direction PB, which would carry it to B 
in the time the body would fail from P to A ; then un- 
der the influence of both forces it would descend along 
the curve PD. If a stronger impulse were given it in 



132. Explain figure 28. How might a body be made to 
circulate quite around the earth? 



104 



UNIVERSAL GRAVITATION. 




the direction PB, it would describe a larger curve PE, 
or PF, or finally, it would go quite round the earth and 
return again to P. 

133. The most simple example we have of the com- 
bined action of these two forces, is the motion of a mis- 
sile thrown from the hand, or of a ball fired from a can- 
non. It is well known that the particular form of the 
curve described by the projectile, in either case, will de- 
pend upon the velocity with which it is thrown. In 
each case the body will begin to move in the line of di- 
rection in which it is projected, but it will soon be de- 
flected from that line towards the earth. It will how- 
ever continue nearer to the line of projection as the ve- 

Fig. 29. 



-B 



W 



locity of projection is greater. 




Thus let AB (Fig. 29,) 



133. When a cannon ball is fired with different velocities, 
when is its motion nearest to the line of projection? 



MOTION IN AN ELLIPTICAL ORBIT. 



105 



perpendicular to AC represent the line of projection. 
The body will, in every case, commence its motion in 
the line AB, which will therefore be the tangent to the 
curve it describes ; but if it be thrown with a small ve- 
ocity, it will soon depart from the tangent, describing 
the line AD ; with a greater velocity it will describe a 
curve nearer to the tangent, as AE ; ' and with a still 
greater velocity it will describe the curve AF. 

134. In figure 30, suppose the planet to have passed 
the point C with so small a velocity,- that the attraction 
of the sun bends its path very much, and causes it im- 
mediately to begin to approach towards the sun ; the 
sun's attraction will increase its velocity as it moves 
through D, E, and F. For the sun's attractive force on 




the planet, when at D, is acting in the direction DS, 
and, on account of the small inclination of DE to DS, 
the force acting in the line DS helps the planet forward 
in the path DE, and thus increases its velocity. In like 
manner, the velocity of the planet will be continually 
increasing as it passes through E, and F ; and though 



134. Explain the motion of a planet in an elliptical orbit, 
from figure 30. 



106 UNIVERSAL GRAVITATION. 

the attractive force, on account of the planet's nearness, 
is much increased, and tends therefore to make the 
orbit more curved, yet the velocity is also so much in- 
creased that the orbit is not more curved than before. 
The same increase of velocity occasioned by the planet's 
approach to the sun, produces a greater increase of cen- 
trifugal force which carries it off again. "We may see 
also why, when the planet has reached the most distant 
parts of its orbit, it does not entirely fly off, and never 
return to the sun. For when the planet passes along 
H, K, A, the sun's attraction retards the planet, just as 
gravity retards a ball rolled up hill ; and when it has 
reached C, its velocity is very small, and the attraction 
at the center of force causes a great deflection from the 
tangent, sufficient to give its orbit a great curvature, 
and the planet turns about, returns to the sun, and goes 
over the same orbit again. As the planet recedes from 
the sun, its centrifugal force diminishes faster than the 
force of gravity, so that the latter finally preponderates. 

135. We may imitate the motion of a body in its orbit 
by suspending a small ball from the ceiling by a long string. 
The ball being drawn out of its place of rest, (which is 
directly under the point of suspension,) it will tend con- 
stantly towards the same place by a force which corres- 
ponds to the force of attraction of a central body. If 
an assistant stands under the point of suspension, his 
head occupying the place of the ball when at rest, the 
ball may be made to revolve about his head as the earth 
or any planet revolves about the sun. By projecting the 
ball in different directions, and with different degrees of 
velocity, we may make it describe different orbits, ex- 
emplifying principles which have been explained in the 
foregoing articles. 



135. How may we imitate the motion of a body in its or- 
bit 1 How may we make the bail describe different orbits ? 



PRECESSION OF THE EQUINOXES. 107 

PRECESSION OF THE EQUINOXES. 

136 The Precession of the equinoxes, is a slow 
but continual shifting of the equinoctial points from east 
to west. 

Suppose that we mark the exact place in the heavens 
where, during the present year, the sun crosses the equa- 
tor, and that this point is close to a certain star ; next 
year the sun will cross the equator a little way west- 
ward of that star, and thus every year a little farther west- 
ward, so that in a long course of ages, the place of the 
equinox will occupy successively every part of the eclip- 
tic, until we come round to the same star again. As, 
therefore, the sun, revolving from west to east in his ap- 
parent orbit, comes round towards the point where it 
left the equinox, it meecs the equinox before it reaches 
that point. The appearance is as though the equinox 
goes forward to meet the sun, and hence the phenome- 
non is called the Precession of the Equinoxes, and the 
fact is expressed by saying that the equinoxes retrograde 
on the ecliptic, until the line of the equinoxes makes a 
complete revolution from east to west. The equator is 
conceived as sliding westward on the ecliptic, always 
preserving the same inclination to it, as a ring placed at 
a small angle with another of nearly the same size, 
which remains fixed, may be slid quite around it, giving 
a corresponding motion to the two points of intersec- 
tion. It must be observed, however, that this mode of 
conceiving of the precession of the equinoxes is purely 
imaginary, and is employed merely for the convenience 
of representation. 

137. The amount of precession annually is 50. "1 ; 
whence, since there are 3600" in a degree, and 360° in 



136. Precession of the Equinoxes. — Define it. If the son 
crosses the equator near a certain star this year, where will it 
cross it next year 1 Why ' ! s the fact called the precession of 
the equinoxes 1 How is the equator conceived as moving 
with regard to the ecliptic ? 



108 UNIVERSAL GRAVITATION. 

the whole circumference, and consequently, 1296000", 
this sum divided by 50.1 gives 25868 years for the pe- 
riod of a complete revolution of the equinoxes. 

138. Suppose now we fix to the center of each "of the 
two rings, (Art. 136,) a wire representing its axis, one 
corresponding to the axis of the ecliptic, the other to 
that of the equator, the extremity of each being the pole 
of its circle. As the ring denoting the equator turns 
round on the ecliptic, which with its axis remains fixed, 
it is easy to conceive that the axis of the equator re- 
volves around that of the ecliptic, and the pole of the 
equator around the pole of the ecliptic, and constantly at 
a distance equal to the inclination of the two circles. To 
transfer our conceptions to the celestial sphere, we may 
easily see that the axis of the diurnal sphere, (that of 
the earth produced, Art. 15,) would not have its pole 
constantly in the same place among the stars, but that 
this pole would perform a slow revolution around the 
pole of the ecliptic from east to west, completing the cir- 
cuit in about 26,000 years. Hence the star which we 
now call the pole star, has not always enjoyed that dis- 
tinction, nor will it always enjoy it hereafter. When 
the earliest catalogues of the stars were made, this star 
was 12° from the pole. It is now 1° 33', and will ap- 
proach still nearer ; or to speak more accurately, the pole 
will come still nearer to this star, after which it will 
leave it, and successively pass by others. In about 
13,000 years, the bright star « Lyree, which lies on the 
circle of revolution opposite to the present pole star, 



137. What is the amount of precession annually? In what 
time will the equinoxes perform a complete revolution ? 

138. Illustrate the precession of the equinoxes by an appa- 
ratus of wires. How is the pole of the earth situated with 
respect to the stars at different times 1 Has the present pole 
star always been such ? What will be the pole star 13,000 
years hence ? Will this cause affect the elevation of tho 
north pole above the horizon ? 



r 



PRECESSION OF THE EQUINOXES. 109 

will be within 5° of the pole, and will constitute the 
Pole Star. As a Lyrse now passes near our zenith, the 
learner might suppose that the change of position of the 
pole among the stars, would be attended with a change 
of altitude of the north pole above the horizon. This 
mistaken idea is one of the many misapprehensions 
which result from the habit of considering the horizon 
as a fixed circle in space. However the pole might 
shift its position in space, we should still be at the 
same distance from it, and our horizon would always 
reach the same distance beyond it. 

139. The time occupied by the sun in passing from 
the equinoctial point round to the same point again, is 
called the tropical year. As the sun does not perform 
a complete revolution in this interval but falls short of it 
50." 1, the tropical year is shorter than the sidereal by 
20m. 20s. in mean solar time, this being the time of de- 
scribing an arc of 5®."\ in the annual revolution.* The 
changes produced by the precession of the equinoxes in 
the apparent places of the circumpolar stars, have led to 
some interesting results in chronology. In consequence 
of the retrograde motion of the equinoctial points, the 
signs of the ecliptic, do not correspond at present to 
the constellations which bear the same names, but lie 
about one whole sign or 30° westward of them. Thus, 
that division of the ecliptic which is called the sign 
Taurus, lies in the constellation Aries, and the sign 
Gemini in the constellation Taurus. Undoubtedly how- 
ever when the ecliptic was thus first divided, and the 
divisions named, the several constellations lay in the re- 
spective divisions which bear their names. How long 
is it, then, since our zodiac was formed ? 



139. Define the tropical year. How much shorter is the 
tropical than the sidereal year 1 How has the precession of the 
equinoxes been applied in Chronology ? 



♦ 59' 8."3 : 24h : . 50."1 : 20m. 20s. 
10 



110 THE MOON. 



50."1 : 1 year: :30°( = 108000 ") : 2155.G years. 
The result indicates that the present divisions of the 
zodiac, were made soon after the establishment of the 
Alexandrian school of astronomy. 



CHAPTER IV. 

OF THE MOON PHASES REVOLUTIONS. 

140. Next to the Sun the Moon naturally claims our 
attention. She is an attendant or satellite to the earth, 
around which she revolves at the distance of nearly 
240,000 miles, or more exactly 238,545 miles. Her 
angular diameter is about half a degree, and her real diam- 
eter 2160 miles. She is therefore a comparatively small 
body, being only one forty-ninth part as large as the 
earth. 

The moon shines by reflected light borrowed from 
the sun, and when full exhibits a disk of silvery bright- 
ness, diversified by extensive portions partially shaded. 
These dusky spots are generally said to be land, and the 
brighter parts water ; but astronomers tell us that if ei- 
ther are water, it must be the darker portions. Land by 
scattering the rays of the sun's light would appear more 
luminous than the ocean which reflects the light like a 
mirror. By the aid of the telescope, we see undoubted 
signs of a varied surface, in some parts composed of ex- 
tensive tracts of level country, and in others exceedingly 
broken by mountains and valleys. 

141. The line which separates the enlightened from 
the dark portions of the moon's disk, is called the Ter- 



140. The Moon. — What relation has the moon to the earth ? 
State her distance, diameter and bulk. Is her light direct or 
reflected ? What are the dark places in the moon generally un- 
derstood to be ? Why would water appear darker than land ? 
What does the telescope reveal to us respecting the moon ? 



LUNAR GEOGRAPHY. Ill 

minator. (See Frontispiece.) As the terminator traver- 
ses the disk from new to full moon, it appears through the 
telescope exceedingly broken in some parts, but smooth 
in others, indicating that portions of the lunar surface are 
uneven while others are level. The broken regions ap- 
pear brighter than the smooth tracts. The latter have 
been taken for seas, but it is supposed with more prob- 
ability that they are extensive plains, since they are still 
too uneven for the perfect level assumed by bodies of 
water. That there are mountains in the moon, is known 
by several distinct indications. First, when the moon 
is increasing, certain spots are illuminated sooner than 
the neighboring places, appearing like bright points be- 
yond the terminator, within the dark part of the disk, 
in the same manner as the tops of mountains on the 
earth are tipped with the light of the sun, in the morn- 
ing, while the regions below are still dark. Secondly, 
after the terminator has passed over them, they project 
shadows upon the illuminated part of the disk, always 
opposite to the sun, corresponding in shape to the form 
of the mountain, and undergoing changes in length from 
night to night, according as the sun shines upon that 
part of the moon more or less obliquely. Many indi- 
vidual mountains rise to a great height in the midst of 
plains, and there are several very remarkable mountain- 
ous groups, extending from a common center in long 
chains. 

142. That there are also valleys in the moon, is 
equally evident. The valleys are known to be truly 
such, particularly by the manner in which the light of 
the sun falls upon them, illuminating the part opposite 
to the sun while the part adjacent is dark, as is the case 
when the light of a lamp shines obliquely into a china 



141. Define the terminator. What do we learn from its rug- 
ged appearance ? State the proofs of mountains in the moon. 

142. State the proofs of valleys in the moon. When is the 
best time for viewing the mountains and valleys of the moon. 



112 THE MOON. 

cup. These valleys are often remarkably regular, and 
some of them almost perfect circles. In several instan- 
ces, a circular chain of mountains surrounds an exten- 
sive valley, which appears nearly level, except that a 
sharp mountain sometimes rises from the center. The 
best time for observing these appearances is near the 
first quarter of the moon, when half the disk is en- 
lightened ;* but in studying the lunar geography, it is 
expedient to observe the moon every evening from new 
to full, or rather through her entire series of changes. 

143. The various places on the moon's disk have re- 
ceived appropriate names. The dusky regions, being 
formerly supposed to be seas, were named accordingly ; 
and other remarkable places have each two names, one 
derived from some well known spot on the earth, and 
the other from some distinguished personage. Thus 
the same bright spot on the surface of the moon is 
called Mount Sinai or Tycho, and another, Mount Et- 
na or Copernicus. The names of individuals, how- 
ever, are more used than the others. The frontispiece 
exhibits the telescopic appearance of the full moon. A 
few of the most remarkable points have the following 
names, corresponding to the numbers and letters on the 
map. (See Fig. p. 113.) 



1. Tycno, 


A. Mare Humorum, 


2. Kepler, 


B. Mare Nubium, 


3. Copernicus, 


C. Mare Imbrium, 


4. Aristarchus, 


D. Mare Nectaris, 


5. Helicon, 


E. Mare Tranquilitatis, 


6. Eratosthenes, 


F. Mare Serenitatis, 


7. Plato, 


G. Mare Fecunditatis, 


8. Archimedes, 


H. Mare Crisium. 


9. Eudoxus, 




10. Aristotle, 





* It is earnestly recommended to the student of astronomy, to exam- 
ine the moon repeatedly with the hest telescope he can commajad, using 
low powers at first, for the sake of a better light. 



TU 






Telescopic view of the Moon. 




TelescDpic view of the Moon when five days old. 



LUNAR GEOGRAPHY. 113 

The figure represents the appearance of the moon 
in the telescope when Ml and when five days old. 
In the latter cut, the learner will remark the rough, 
rugged appearance of the terminator ; the illuminated 
points beyond the terminator within the dark part of the 
moon, which are the tops of mountains; and the nu- 
merous circular spaces, which exhibit valleys or caverns 
surrounded by mountainous chains. Those circles which 
are near the terminator into which the suns light shines 
very obliquely, cast deep shadows on the sides opposite 
the sun. Those more remote from the terminator, and 
farther within the illuminated part of the moon, into 
which the sun shines more directly, have a greater por- 
tion illuminated, with shorter shadows ; and those which 
lie near the edge of the moon, most distant from the ter- 
minator, are of an oval figure, being presented obliquely 
to the eye. 

144. The heights of the lunar mountains, and the 
depths of the valleys, can be estimated with a considera- 
ble degree of accuracy. Some of the mountains are as 
high as five miles, and the valleys in some instances 
are four miles deep. Hence it is inferred that the sur- 
face of the moon is more broken and irregular than that 
of the earth, its mountains being higher and its valleys 
deeper in proportion to its magnitude than that of the 
earth. The lunar mountains in general, exhibit an ar- 



143. How are places in the moon named ? Point out the 
most remarkable places on the map of the full moon. Point 
out the mountains, valleys, and craters, on the cut, which rep- 
resents the moon five days old. 

144. Specify the heights of some of the lunar mountains. 
Is the surface of the moon more or less broken than that of the 
earth 1 Are the mountains like or unlike ours ? What is the 
first variety ? What is the shape of the insulated mountains ? 
How can their heights be calculated 1 What is said of the 
second variety, the mountain ranges 1 What is said of the 
circular ranges ? What is said of the central mountains ? 

, 10* 



114 THE MOON. 

rangement and an aspect very different from the moun- 
tain scenery of our globe. They may be arranged un- 
der the four following varieties. 

First, Insulated Mountains, which rise from plains 
nearly level, shaped like a sugar loaf, which may be 
supposed to present an appearance somewhat similar to 
Mount Etna, or the Peak of Teneriffe. The shadows 
of these mountains, in certain phases of the moon, are 
as distinctly perceived, as the shadow of an upright staff, 
when placed opposite to the sun ; and these heights can 
be calculated from the length of their shadows. Some 
of these mountains being elevated in the midst of exten- 
sive plains, would present to a spectator on their sum- 
mits, magnificent views of the surrounding regions. 

Secondly, Mountain Ranges, extending in length two 
or three hundred miles. These ranges bear a distant re- 
semblance to our Alps, Appenines, and Andes ; but they 
are much less in extent. Some of them appear very 
rugged and precipitous, and the highest ranges are in 
some places more than four miles in perpendicular alti- 
tude. In some instances, they are nearly in a straight 
line from northeast to southwest, as in that range called 
the Appenines ; in other cases they assume the form of 
a semicircle or crescent. 

Thirdly, Circular Ranges, which appear on almost 
every part of the moon's surface, particularly in its south- 
ern regions. This is one grand peculiarity of the lunar 
ranges, to which we have nothing similar on the earth. 
A plain, and sometimes a large cavity, is surrounded 
with a circular ridge of mountains, which encompasses 
it like a mighty rampart. These annular ridges and 
plains are of all dimensions, from a mile to forty or fifty 
miles in diameter, and are to be seen in great numbers 
over every region of the moon's surface ; they are most 
conspicuous, however, near the upper and lower limbs 
about the time of half moon. 

The mountains which form these circular ridges are 
of different elevations, from one fifth of a mile to three 
and a half miles, and their shadows cover one half of 
the plain at the base. These plains are sometimes on 



LUNAR GEOGRAPHY. 115 

a level with the general surface of the moon, and in 
other cases they are sunk a mile or more below the level 
of the ground, which surrounds the exterior circle of the 
mountains. 

Fourthly, Central Mountains, or those which are 
placed in the middle of circular plains. In many of the 
plains and cavities surrounded by circular ranges of 
mountains there stands a single insulated mountain, 
which rises from the center of the plain, and whose 
shadow sometimes extends in the form of a pyramid 
half across the plain or more to the opposite ridges. 
These central mountains are generally from half a mile 
to a mile and a half in perpendicular altitude. In some 
instances they have two and sometimes three different 
tops, whose shadows can be easily distinguished from 
each other. Sometimes they are situated towards one 
side of the plain or cavity, but, in the great majority 
of instances, their position is nearly or exactly central. 
The lengths of their bases vary from five to about fifteen 
or sixteen miles. 

145. The Lunar Caverns form a very peculiar and 
prominent feature of the moon's surface, and are to 
be seen throughout almost every region, but are most 
numerous in the southwest part of the moon. Nearly a 
hundred of them, great and small, may be distinguished 
in that quarter. They are all nearly of a circular shape, 
and appear like a very shallow egg-cup. The smaller 
cavities appear within almost like a hollow cone, with 
the sides tapering towards the center ; but the larger 
ones have for the most part, flat bottoms, from the cen- 
ter of which there frequently rises a small steep conical 
hill, which gives them a resemblance to the circular 
ridges and central mountains before described. In some 
instances their margins are level with the general sur- 
face of the moon, but in most cases they are encircled 



145. Lunar Caverns. — What is said of their number, shape 
and appearances ? 



116 THE MOON. 

with a high annular ridge of mountains, marked with 
lofty peaks. Some of the larger of these cavities con 
tain smaller cavities of the same kind and form, particu- 
larly in their sides. The mountainous ridges which sur- 
round these cavities, reflect the greatest quantity of 
light ; and hence that region of the moon in which they 
abound, appears brighter than any other. From their 
lying in every possible direction, they appear at and 
near the time of full moon, like a number of brilliant 
streaks or radiations. These radiations appear to con- 
verge towards a large brilliant spot, surrounded by a 
faint shade, near the lower part of the moon which is 
named Tycho, (Frontispiece, 1,) which may be easily dis- 
tinguished even by a small telescope. The spots named 
Kepler and Copernicus, are each composed of a central 
spot with luminous radiations.* 

146. Dr. Herschel is supposed also to have obtained 
decisive evidence of the existence of volcanoes in the 
moon, not only from the light afforded by their fires, 
but also from the formation of new mountains by the 
accumulation of matter where fires had been seen to 
exist, and which remained after the fires were extinct. 

147. Some indications of an atmosphere about the 
moon have been obtained, the most decisive of which 
are derived from appearances of twilight, a phenomenon 
that implies the presence of an atmosphere. Similar in- 
dications have been detected, it is supposed, in eclipses 
of the sun, denoting a transparent refracting medium 
encompassing the moon. 



146. Volcanoes. — What proofs are there of their having ex- 
isted in the moon ? 

147. What evidence is there of a lunar atmosphere ? 



* The foregoing accurate description of the lunar mountains and cav- 
erns is from " Dick's Celestial Scenery." 



LUNAR GEOGRAPHI. 117 

148. It has been a question with astronomers, whether 
there is water in the moon ? The general opinion is 
that there is none. If there were any, we should ex- 
pect to see clouds ; or at least we should expect to find 
the face of the moon occasionally obscured by clouds ; 
but this is not the case, since the spots on the moon's 
disk, when our sky is clear, are always in full view. 
The deep caverns, moreover, seen in those dusky spots 
which were supposed to be seas, are unfavorable to the 
supposition, that they are surrounded by water ; and the 
terminator when it passes over these places is, as already 
remarked, too uneven to permit us to suppose that these 
tracts are seas. 

149. The improbability of our ever identifying arti- 
ficial structures in the moon, may be inferred from the 
fact that a line one mile in length in the moon subtends 
an angle at the eye of only about one second. If, there- 
fore, works of art were to have a sufficient horizontal 
extent to become visible, they can hardly be supposed 
to attain the necessary elevation, when we reflect that 
whe height of the great pyramid of Egypt is less than 
the sixth part of a mile. Still less probable is it that we 
shall ever discover any inhabitants in the moon. The 
greatest magnifying power that has ever been applied 
with distinctness, to the moon, does not much exceed a 
thousand times, bringing the moon apparently a thou- 
sand times nearer to us than when seen by the naked 
eye. But this implies a distance still of 240 miles ; and 



148. Is there water in the moon ? What proofs arc there 
to the contrary 1 

149. Is it probable that artificial structures in the moon will 
ever be identified ? How high must they be, in order to be 
seen distinct from the surface ? Is it probable that we shall 
ever be able to recognize inhabitants in the moon ? What is 
the greatest magnifying power of the telescope that has ever 
been applied to the moon ? If we could magnify the moon 
1 0,000 times what would still be her apparent distance ? What 
inherent difficulty is there in employing very great magnifiers ? 



118 THE MOON. 

could we magnify the moon ten thousand times, her ap- 
parent distance would still be twenty-four miles, a dis- 
tance too great to distinguish living beings. Moreover, 
when we use such high magnifiers in the telescope, our 
field of view is necessarily exceedingly small, so that it 
would be a mere point that we could view at a time. 
This difficulty is inherent in the very nature of tele- 
scopes, namely, that the field of view is reduced as the 
magnifying power is increased ; and we magnify the 
vapors and the undulations of the atmosphere, as well 
as the moon, and by this means impair the medium so 
much that we should not be able to see anything with 
distinctness. It is only to such minute objects as a star, 
that very high powers of the telescope can ever be ap- 
plied. 

150. Some writers, however, suppose that possibly 
we may trace indications of lunar inhabitants in their 
works, and that they may, in like manner, recognize the 
existence of the inhabitants of our planet. An author 
who has reflected much on subjects of this kind, rea- 
sons as follows : A navigator who approaches within a 
certain distance of a small island, although he perceives 
no human being upon it, can judge with certainty, that 
it is inhabited, if he perceives human habitations, villa- 
ges, cornfields, or other traces of cultivation. In like 
manner, if we could perceive changes or operations in 
the moon, which could be traced to the agency of intel- 
ligent beings, we should then obtain satisfactory evi- 
dence, that such beings exist on that planet ; and it is 
thought possible that such operations may be traced. 
A telescope which magnifies 1200 times, will enable us 
to perceive, as a visible point on the surface of the moon, 
an object whose diameter is only about 300 feet. Such 



150. What have some writers supposed with respect to the 
probability of our tracing marks of living beings on the moon ? 
How is it proposed to ha^e thfl moon examined for this pur- 
pose I 



LUNAR GEOGRAPHY. 119 

an object is not larger than many of our public edifices ; 
and, therefore, were any such edifices rearing in the 
moon, or were a town or city extending its boundaries, 
or were operations of this description carrying on in a 
district where no such edifices had previously been 
erected, such objects and operations might probably be 
detected by a minute inspection. Were a multitude of 
living creatures moving from place to place in a body, 
or were they even encamping in an extensive plain, like 
a large army, or like a tribe of Arabs in the desert, and 
afterwards removing, it is possible that such changes 
might be traced by the difference of shade or color, 
which such movements would produce. In order to de- 
tect such minute objects and operations, it would be 
requisite that the surface of the moon should be distrib- 
uted among at least a hundred astronomers, each having 
a spot or two allotted to him, as the object of his more 
particular investigation, and that the observations be 
continued for a period of at least thirty or forty years, 
during which time certain changes would probably be 
perceived, arising either from physical causes, or from 
the operations of living agents.* 

151. It has sometimes been a subject of speculation, 
whether it might be possible, by any symbols, to cor- 
respond with the inhabitants of the moon. It has been 
suggested, that if some vast geometrical figure, as a 
square or a triangle, were erected on the plains of Siberia, 
it might be recognized by the lunarians, and answered 
by some corresponding signal. Some geometrical figure 
would be peculiarly appropriate for such a telegraphic 
commerce with the inhabitants of another sphere, since 
these are simple ideas common to all minds. 



151. How is it proposed to carry on a telegraphic communi- 
cation with the lunarians ? 



* Dick's Celestial Scenery, Ch. iv. 



r20 THE MOON. 

PHASES OF THE MOON. 

152. The changes of the moon, commonly called her 
Phases, arise from different portions of her illuminated 
side being turned towards the earth at different times. 
When the moon is first seen after the setting sun, her 
form is thit of a bright crescent, on the side of the disk 
next to the sun, while the other portions of the disk 
shine with a feeble light, reflected to the moon from the 
earth. Every night we observe the moon to be farther 
and farther eastward of the sun, and at the same time 
the crescent enlarges, until, when the moon has reached 
an elongation from the sun of 90°, half her visible disk 
is enlightened, and she is said to be in her first quarter. 
The terminator, or line which separates the illuminated 
from the dark part of the moon, is convex towards the 
sun from the new moon to the first quarter, and the 
moon is said to be horned. The extremities of the 
crescent are called cusps. At the first quarter, the ter- 
minator becomes a straight line, coinciding with a di- 
ameter of the disk ; but after passing this point, the ter- 
minator becomes concave towards the sun, bounding 
that side of the moon by an elliptical curve, when the 
moon is said to be gibbous. When the moon arrives at 
the distance of 180° from the sun, the entire circle is 
illuminated, and the moon is full. She is then in oppo- 
sition to the sun, rising about the time the sun sets. For 
a week after the full, the moon appears gibbous again, 
until, having arrived within 90° of the sun, she re- 
sumes the same form as at the first quarter, being then 
at her third quarter. From this time until new moon, 
she exhibits again the form of a crescent before the ri- 
sing sun, until, approaching her conjunction with the 



152. Phases of the Moon. — Whence do they rise ? State 
the successive appearances of the moon from new to full. In 
what parts of her revolution is she horned, and in what parts 
gibbons ? When is she said to be in conjunction, and when in 
opposition ? What are the syzigies, quadratures, and octants ? 
Define the circle of illumination, and the ciicle of the disk. 






PHASES. 121 

sun, her narrow thread of light is lost in the solar blaze ; 
and finally, at the moment of passing the sun, the dark 
side is wholly turned towards us, and for some time we 
lose sight of the moon. 

The two points in the orbit corresponding to new and 
full moon respectively, are called by the common name 
of syzigies ; those which are 90° from the sun are 
called quadratures ; and the points half way between 
the syzigies and quadratures are called octants. The 
circle which divides the enlightened from the unen- 
lightened hemisphere of the moon, is called the circle of 
illumination: that which divides the hemisphere that 
is turned towards us from the hemisphere that is turn- 
ed from us, is called the circle of the disk. 

153. As the moon is an opake body of a spherical 
figure, and borrows her light from the sun, it is obvious 

Fig. 31 




that that half only which is towards the sun can be il- 
luminated. More or less of this side is turned towards 
the earth, according as the moon is at a greater or less 
elongation from the sun. The reason of the different 
phases will be best understood from a diagram. There- 
fore let T (Fig. 31.) represent the earth, and S the sun. 
. 11 



122 THE MOON. 

Let A, B, C, &c. be successive positions of the moon. 
At A the entire dark side of the moon being turned to- 
wards the earth, the disk would be wholly invisible. Al 
B, the circle of the disk cuts of a small part of the en 
lightened hemisphere, which appears in the heavens at 
b, under the form of a crescent. At C, the first quarter 
the circle of the disk cuts off half the enlightened hem- 
isphere, and a half moon is seen at c. In like manner it 
will be seen that the appearances presented at D, E, F, 
&c. must be those represented at d, e,f. If a round 
body, as an apple, suspended by a string, be carried 
around a lamp, the eye remaining fixed opposite to it at 
the same level, the various phases of the moon will be 
exhibited. 

REVOLUTIONS OF THE MOON. 

154. The moon revolves around the earth from west 
to east, making the entire circuit of the heavens in about 
27} days. 

The period of the moon's revolution from any point 
in the heavens round to the same point again, is called 
a month. A sidereal month is the time of the moon's 
passing from any star, until it returns to the same star 
again. A synodical month, so called from two Greek 
words implying that at the end of this period the two 
bodies (the sun and moon) come together, is the time 
from one conjunction or new moon to another. The 
synodical month is about 29J days, or more exactly, 
29d. 12h. 44m. 2s.8 =29.53 days. The sidereal month 
is about two days shorter, being 27d. 7h. 43m. lls.5. 
or 27.32 days. As the sun and moon are both revolv- 
ing in the same direction, and the sun is moving nearly 



153. How much of the moon is illuminated at once? Ex- 
plain the phases of the moon from figure 31. 

154. Define a month. Define a sidereal month. Also a sy- 
nodical month. Why so called ? What is the length of the 
synodical month ? Also of the sidereal month 1 What is the 
moon's daily motion ? 



REVOLUTIONS. 123 

a degree a day, during the 27 days of the moon's revo- 
lution, the sun must have moved 27°. Now since the 
moon passes over 360° in 27.32 days, her daily motion 
must be 13° 17'. It must therefore evidently take about 
two days for the moon to overtake the sun. 

155. The moon's orbit is inclined to the ecliptic in an 
angle of about 5° (5° 8' 48".) The moon crosses the 
ecliptic in two opposite points called her nodes. That 
which the moon crosses from south to north, is called 
her ascending node, that which she crosses from north 
to south, her descending node. The moon, therefore, is 
never seen far from the ecliptic, but the path she pur- 
sues through the skies, is very nearly the same as that 
of the sun in his annular revolution around the earth. 

156. The moon, at the same age, crosses the meridian 
at different altitudes at different seasons of the year ; and 
accordingly it is said to run sometimes high and some- 
times low. The full moon, for example, will appear 
much farther in the south when on the meridian at one 
period of the year than at another. The reason of this 
may be explained as follows. When the sun is in the 
part of the ecliptic south of the equator, "the earth and 
of course the moon, which always keeps near to the 
earth, is in the part north of the equator. At such 
times, therefore, the new moons, which are always 
seen in the part of the heavens where the sun is, will 
run far south, while the full moons, which are always in 
the opposite part of the heavens from the sun, will run 
high. Such is the case during the winter months ; but. 



1 55. How much is the moon's orbit inclined to the ecliptic ? 
Define the nodes. What is the ascending and Avhat the de- 
scending node ? 

156. Why does the moon run high and low ? At what sea- 
son of the year are the full moons longest above the horizon ? 
Explain how this operates favorably to those who are near 
the pole. 



124 THE MOON. 

in the summer, when the sun is towards the northern 
tropic and the earth towards the southern, the new 
moons run high and the full moons low. This arrange- 
ment gives us a great advantage in respect to the amount 
of light received from the moon ; since the full moon 
is longest above the horizon during the long nights of 
winter, when her presence is most needed, This cir- 
cumstance is especially favorable to the inhabitants of 
the polar regions, the moon, when full, traversing that 
part of her orbit which lies north of the equator, and of 
course above the horizon of the north pole, and traver- 
sing the portion that lies south of the equator, and be- 
low the polar horizon, when new. During the polar 
winter, therefore, the moon, during her second and third 
quarters, when she gives most light, is commonly above 
the horizon, while the sun is absent ; whereas, during 
summer, while the sun is present and the light is not 
needed, during her second and third quarters, she is be- 
low the horizon. 

157. About the time of the autumnal equinox, the 
moon when near the full, rises about sunset for a num- 
ber of nights in succession ; and as this is, in England, 
the period of' harvest, the phenomenon is called the 
Harvest Moon. To understand the reason of this, since 
the moon is never far from the ecliptic, we will suppose 
her progress to be in the ecliptic. If the moon moved 
in the equator, then, since this great circle is at right 
angles to the axis of the earth, all parts of it, as the 
earth revolves, cut the horizon at the same constant 
angle. But the moon's orbit, or the ecliptic, which is 
here taken to represent it, being oblique to the equator, 
cuts the horizon at different angles in different parts, as 
will easily be seen by reference to an artificial globe. 
When the first of Aries, or vernal equinox, is in the 



157. Why is the harvest moon so called ? Explain its cause. 
How is the moon's orbit inclined to the horizon at different 
times ? 



REVOLUTIONS. 125 

eastern horizon, it will be seen that the ecliptic, (and 
consequently the moon's orbit,) makes its least angle 
with the horizon. Now, at the autumnal equinox, the 
sun being in Libra, the moon at the full, when she is 
always opposite to the sun, is in Aries, and rises when 
the sun sets. On the following evening, although she 
has advanced in her orbit about 13°, yet her progress be- 
ing oblique to the horizon, and at a small angle with it, 
she will be found at this time but a little w T ay below the 
horizon, compared with the point where she was at sun- 
set the preceding evening. She therefore rises but little 
later, and so for a week only a little later each evening 
than she did the preceding night. 

1 58. The moon turns on its axis in the same time in 
which it revolves around the earth. 

This is known by the moon's always keeping nearly 
the same face towards us, as is indicated by the tele- 
scope, which could not happen unless her revolution on 
her axis kept pace with her motion in her orbit. Thus 
it will be seen by inspecting figure 22, that the earth 
turns different faces towards the sun at different times ; 
and if a ball having one hemisphere white and the 
other black be carried around a lamp, it will easily be 
seen that it cannot present the same face constantly to- 
wards the lamp unless it turns once on its axis while 
performing its revolution. The same thing will be ob- 
served when a man walks around a tree, keeping his face 
constantly towards it. Since however the motion of 
the moon on its axis is uniform, while the motion in its 
orbit is unequal, the moon does in fact reveal to us a lit- 
tle sometimes of one side and sometimes of the other. 
Thus when the ball above mentioned is placed before 
the eye with its light side towards us, on carrying it 
round, if it is moved faster than it is turned on its axis, 



]58. In what time does the moon turn on its axis ? Illus- 
trate by the motion of a ball around a lamp. Is the same side 
of the moon ahravs turned exactly towards us 1 

11* 



126 1HE MOON. 

a portion of the dark hemisphere is brought into view 
on one side ; or if it is moved forward slower than it is 
turned on its axis, a portion of the dark hemisphere 
comes into view on the other side. 

159, These appearances are called the moon's libra- 
tions in longitude. The moon has also a libration in 
latitude, so called, because in one part of her revolution, 
more of the region around one of the poles comes into 
view, and in another part of the revolution, more of the 
region around the other pole ; which gives the appear- 
ance of a tilting motion to the moon's axis. This has 
nearly the same cause with that which occasions our 
change of seasons. The moon's axis being inclined to 
the plane of her orbit, and always remaining parallel to 
itself, the circle which divides the visible from the in- 
visible part of the moon, will pass in such a way as to 
throw sometimes more of one pole into view, and some- 
times more of the other, as would be the case with the 
earth if seen from the sun. (See Fig. 22.) 

The moon exhibits another phenomenon of this kind 
called her diurnal libration, depending on the daily ro- 
tation of the spectator. She turns the same face to- 
wards the center of the earth only, whereas we view 
her from the surface. When she is on the meridian, we 
see her disk nearly as though we viewed it from the 
center of the earth, and hence in this situation it is sub- 
ject to little change ; but when near the horizon, our 
circle of vision takes in more of the upper limb than 
would be presented to a spectator at the center of the 
earth. Hence, from this cause, we see a portion of one 
limb while the moon is rising, which is gradually lost 
sight of, and we see a portion of the opposite limb as 
the moon declines to the west. It will be remarked 
that neither of the foregoing changes implies any actual 
motion in the moon, but that each arises from a change 
of position in the spectator. 



159. Explain -he librations in longitude. Ditto in latilado 
Ditto the diurnal librations. 



REVOLUTIONS. 127 

160. Since the succession of day and night depends 
on the revolution of a planet on its own axis, an inhab- 
itant of the moon would have but one day and one night 
during the whole lunar month of 29^- days. One of its 
days, therefore, is equal to nearly 15 of ours. So pro- 
tracted an exposure to the sun's rays, especially in the 
equatorial regions of the moon, must occasion an exces- 
sive accumulation of heat ; and so long an absence of 
the sun must occasion a corresponding degree of cold. 
Each day would be a wearisome summer ; each night a 
severe winter.* A spectator on the side of the moon 
which is opposite to us would never see the earth ; but 
one on the side next to us would see the earth present- 
ing a gradual succession of changes during his long 
night of 380 hours. Soon after the earth's conjunction 
with the sun, he would have the light of the earth re- 
flected to him, presenting at first a crescent, but enlarg- 
ing as the earth approaches its opposition, to a great orb, 
13 times as large as the full moon appears to us, and af- 
fording nearly 13 times as much light. Our seas, our 
plains, our mountains, our volcanoes, and our clouds, 
would produce very diversified appearances, as would 
the various parts of the earth brought successively into 
view by its diurnal rotation. The earth while in view 
to an inhabitant of the moon, would remain immovably 
fixed in the same part of the heavens. For being un- 
conscious of his own motion around the earth, as we are 
of our motion around the sun, the earth would seem to 
revolve around his own planet from west to east, just as 
the moon appears to us to revolve about the earth ; but, 
meanwhile, his rotation along with the moon on her 
axis, would cause the earth to have an apparent motion 



160. How many days would an inhabitant of the moon have 
in a lunar month ? What vicissitudes of temperature would 
occur in a single day ? Would a spectator on the side of the 
moon opposite to us, ever see the earth ? How wouldthe earth 
appear to a spectator on the side of the moon next to us ? 



Francoeur, Uratiog. p. 91. 



128 THE MOON. 

westward at the same rate. The two motions, there- 
fore, would exactly balance each other, and the earth 
would appear all the while at rest. 

161. We have thus far contemplated the revolution 
of the moon around the earth as though the earth were 
at rest. But, in order to have just ideas respecting the 
moon's motions, we must recollect that the moon like- 
wise revolves along with the earth around the sun. It 
is sometimes said that the earth carries the moon along 
with her in her annual revolution. This language may 
convey an erroneous idea ; for the moon, as well as the 
earth, revolves around the sun under the influence of 
two forces, and would continue her motion around the 
sun were the earth removed out of the way. Indeed, 
the moon is attracted towards the sun 2J times more 
than towards the earth, and would abandon the earth 
were not the latter also carried along with her by the 
same forces. So far as the sun acts equally on both 
bodies, their motion with respect to each other would 
not be disturbed. Because the gravity of the moon to- 
wards the sun is found to be greater, at the conjunction, 
than her gravity towards the earth, some have appre- 
hended that, if the doctrine of universal gravitation is 
true, the moon ought necessarily to abandon the earth. 
In order to understand the reason why it does not do 
thus, we must reflect, that when a body is revolving in 
its orbit under the action of the projectile force and 
gravity, whatever diminishes the force of gravity while 
that of projection remains the same, causes the body to 
approach nearer to the tangent of her orbit, and of course 
to recede from the center ; and whatever increases the 
amount of gravity carries the body towards the center. 



161. Can it be said that the earth carries the moon around 
the sun ? How much more is the moon attracted towards the 
sun than towards the earth ? Why does not the moon abandon 
the earth ? When the sun acts equally on both bodies, does it 
disturb their relative places? How does the sun act upon 
these bodies at the conjunctions and oppositions ? 



REVOLUTIONS. 129 

Now, when the moon is in conjunction, her gravity to- 
wards the earth acts in opposition to that towards the 
sun, while her velocity remains too great to carry her, 
with what force remains, in a circle about the sun, and 
she therefore recedes from the sun, and commences her 
revolution around the earth. On arriving at the opposi- 
tion, the gravity of the earth conspires with that of the 
sun, and the moon's projectile force being less than that 
required to make her revolve in a circular orbit, when 
attracted towards the sun by the sum of these forces, she 
accordingly begins to approach the sun and descends 
again to the conjunction. 

162. The attraction of the sun, however, being every 
where greater than that of the earth, the actual path of 
the moon around the sun is every where concave to- 
wards the latter. Still the elliptical path of the moon 
around the earth, is to be conceived of in the same way 
as though both bodies were at rest with respect to the 
sun. Thus, while a steamboat is passing swiftly around 
an island, and a man is walking slowly around a post in 
the cabin, the line which he describes in space between 
the forward motion of the boat and his circular motion 
around the post, may be every where concave towards 
the island, while his path around the post will still be 
the same as though both were at rest. A nail in the rim 
of a coach wheel, will turn around the axis of the wheel, 
when the coach has a forward motion in the same man- 
ner as when the coach is at rest, although the line ac- 
tually described by the nail will be the resultant of both 
motions, and very different from either. 

163. We have hitherto regarded the moon as descri- 
bing a great circle on the face of the sky, such being the 



162. How is the moon's path in space with respect to the 
sun ? How is the elliptical path of the moon around the earth 
to be conceived of 1 How is this illustrated by the motions of 
a man in a steamboat ? Also by the motions of a nail in the 
rim of a coach wheel ? 



130 THE MOON. 

visible orbit as seen by projection. But, on more exact 
investigation, it is found that her orbit is not a circle, 
and that her motions are subject to very numerous ir- 
regularities. These will be best understood in connec- 
tion with the causes on which they depend. The law 
of universal gravitation has been applied with wonder- 
ful success to their investigation, and its results have 
conspired with those of long continued observation, to 
furnish the means of ascertaining with great exactness 
the place of the moon in the heavens at any given in- 
stant of time, past or future, and thus to enable astrono- 
mers to determine longitudes, to calculate eclipses, and 
to solve various other problems of the highest interest. 
A complete understanding of all the irregularities of the 
moon's motions, must be sought for in more extensive 
treatises of astronomy than the present ; but some gen- 
eral acquaintance with the subject, clear and intelligible 
as far as it goes, may be acquired by first gaining a dis- 
tinct idea of the mutual actions of the sun, the moon, 
and the earth. 

164. The irregularities of the moon's motions, are 
due chiefly to the disturbing influence of the sun, which 
operates in two ways ; first, by acting unequally on the 
earth and moon, and, secondly, by acting obliquely on 
the moon, on account of the inclination of her orbit to 
the ecliptic. 

If the sun acted equally on the earth and moon, and 
always in parallel lines, this action would serve only to 
restrain them in their annual motions round the sun, and 
would not affect their actions on each other, or their 
motions about their common center of gravity. In that 
case, if they were allowed to fall directly towards the 
sun, they would fall equally, and their respective situa- 
tions would not be affected by their descending equally 
towards it. We might then conceive them as in a 
plane, every part of which being equally acted on by 



163. Are the motions of the moon regular or irregular ? By 
what, general law are they explained 1 



REVOLUTIONS. 131 

the sun, the whole plane would descend towards the 
sun, but the respective motions of the earth and the 
moon in this plane, would be the same as if it were 
quiescent. Supposing then this plane and all in it, 
to have an annual motion imprinted on it, it would 
move regularly around the sun, while the earth and moon 
would move in it with respect to each other, as if the 
plane were at rest, without any irregularities. But be- 
cause the moon is nearer the sun in one half of her orbit 
than the earth is, and in the other half of her orbit is at 
a greater distance than the earth from the sun, while the 
power of gravity is always greater at a less distance ; it 
follows, that in one half of her orbit the moon is more 
attracted than the earth towards the sun, and in the other 
half less attracted than the earth. The excess of the 
attraction, in the first case, and the defect in the second, 
constitutes a disturbing force, to which we may add an- 
other, namely, that arising from the oblique action of the 
solar force, since this action is not directed in parallel 
lines, but in lines that meet in the center of the sun. 

165. To see the effects of this process, let us suppose 
that the projectile motions of the earth and moon were 
destroyed, and that they were allowed to fall freely to- 
wards the sun. If the moon was in conjunction with 
the sun, or in that part of her orbit which is nearest to 
him, the moon would be more attracted than the earth, 
and fall with greater velocity towards the sun ; so that 
the distance of the moon from the earth w T ould be in- 
creased in the fall. If the moon was in opposition, or 



164. To what cause are the inequalities of the moons mo- 
tions chiefly due ? If the sun acted equally on the earth and 
moon, and in parallel lines, would it disturb their motions ? If 
allowed to fair towards the sun, how would they fall? How 
might we conceive them as situated in a plane ? When is the 
moon more attracted than the earth ? When is the earth more 
attracted than the moon 1 What constitutes the disturbing face. 

165. Trace the effects of the sun, if the projectile force were 
destroyed, at conjunction, at opposition, and at quadrature. 



132 THE MOON. 

in the part of her orbit which is farthest from the sun, 
she would be less attracted than the earth by the sun, 
and would fall with a less velocity towards the sun, and 
would be left behind ; so that the distance of the moon 
from the earth would be increased in this case also. If 
the moon was in one of the quarters, then the earth and 
moon being both attracted towards the center of the 
sun, they would both descend directly towards that cen- 
ter, and by approaching it, they would necessarily at 
the same time approach each other, and in this case their 
distance from each other would be diminished. Now 
whenever the action of the sun would increase their dis- 
tance, if they were allowed to fall towards the sun, 
then the sun's action, by endeavouring to separate them, 
diminishes their gravity to each other ; whenever the 
sun's action would diminish the distance, then it in- 
creases their mutual gravitation. Hence, in the con- 
junction and opposition, that is, in the syzigies, their 
gravity towards each other is diminished by the action 
of the sun, while in the quadratures it is increased. 
But it must be remembered that it is not the total action 
of the sun on them that disturbs their motions, but only 
that part of it which tends at one time to separate them, 
and at another time to bring them nearer together. The 
other and far greater part, has no other effect than to 
retain them in their annual course around the sun. 

166. The figure of the moon's orbit is an ellipse, hav- 
ing the earth in one of the foci. 

The greatest and least distances of the moon from the 
earth, are nearly 64 and 56, the radius of the earth being 
taken for unity. Hence, taking the arithmetical mean, 
we find that the mean distance of the moon from the 



166. What is the figure of the moon's orbit ? What are the 
greatest and least distances of the moon from the earth ? De- 
fine the terms perigee and apogee. What numbers express the 
greatest and least distance of the sun from the earth 1 How 
does the eccentricity of the lunar orbit, compare with that of 
the solar 1 



REVOLUTIONS. 133 

earth is very nearly 60 times the radius of the earth. 
The point in the moon's orbit nearest the earth, is 
called her perigee ; the point farthest from the earth, 
her apogee. 

The greatest and least distances of the sun are re- 
spectively as the numbers 32.583, and 31.51 7. By com- 
paring this ratio with that of the distances of the moon, 
it will be seen that the latter vary much more than the 
former, and consequently that the lunar orbit is much 
more eccentric than the solar. The eccentricity of the 
moon's orbit is in fact ~ of its mean distance from the 
earth, while that of the earth is only -^ of its mean dis- 
tance from the sun, 

167. The mooits nodes constantly shift their positions 
in the ecliptic from east to west, at the rate of 19° 3d per 
annum, returning to the same points in 18.6 years. 

Suppose the great circle of the ecliptic marked out on 
the face of the sky in a distinct line, and let us observe, 
at any given time, the exact point where the moon 
crosses this line, which w T e will suppose to be close to a 
certain star ; then, on its next return to that part of the 
heavens, we shall find that it crosses the ecliptic sensi- 
bly to the westward of that star, and so on, farther and 
farther to the westward every time it crosses the ecliptic 
at either node. This fact is expressed by saying that 
the nodes retrograde on the ecliptic, and that the line 
which joins them, or the line of the nodes, revolves from 
east to west. 

1 68. The period occupied by the sun in passing from 
one of the moon's nodes until it comes round to the 
same node again, is called the synodical revolution of the 
node. This period is shorter than the sidereal year, be- 
ing only about 346^ days. For since the node shifts its 



167. How do the moon's nodes shift their position ? In 
what time do they make a complete revolutin in the ecliptic 1 
Explain what is mean* hy saying that the nodes retrogade. 

12 



134 THE MOON. 

place to the westward 19° 35' per annum, the sun, in 
his annual revolution, comes to it so much before he 
completes his entire circuit ; and since the sun moves 
about a degree a day, the synodical revolution of the 
node is 365 — 19=346, or more exactly, 346.619851. 
The time from one new moon, or from one full moon, 
to another, is 29.5305887 days. Now 19 synodical rev- 
olutions of the nodes contain very nearly 223 of these 
periods. 

For 346.619851 x 19 = 6585.78. 

And 29.5305887x223 = 6585.32. 
Hence, if the sun and moon were to leave the moon's 
node together, after the sun had been round to the same 
node 19 times, the moon would have made very nearly 
223 conjunctions with the sun, and would therefore, at 
the end of this period meet at the same node, to repeat 
the same circuit. And since eclipses of the sun and 
moon depend upon the relative position of the sun, the 
moon, and node, these phenomena are repeated in nearly 
the same order, in each of those periods. Hence, this 
period, consisting of about 18 years and 10 days, under 
the name of the Saros, was used by the Chaldeans and 
other ancient nations in predicting eclipses. 

169. The Metonic Cycle is not the same with the Sa- 
ros, but consists of 19 tropical years. During this pe- 
riod the moon makes very nearly 235 synodical revolu- 
tions, and hence the new and full moons, if reckoned 
by periods of 19 years, recur at the same dates. If, for 
example, a new moon fell on the fiftieth day of one 
cycle, it would also fall on the fiftieth day of each suc- 



168. What is meant by the synodical revolution of the node 1 
How many new moons occur in 19 synodical revolutions of the 
node 1 Why was this period used in predicting eclipses ? What 
was it called ? 

169. What is the period of the Metonic Cycle 1 How many 
conjunctions of the moon with the sun occur during this pe- 
riod ? What us$ did the Athenians make of this lunar cycle 1 



REVOLUTIONS. 135 

ceeding cycle ; and, since the regulation of games, 
feasts, and fasts, has been made very extensively ac- 
cording to new or full moons, hence this lunar cycle has 
been much used both in ancient and modern times. 
The Athenians adopted it 433 years before the Christian 
era, for the regulation of their calendar, and had it in- 
scribed in letters of gold on the walls of the temple of 
Minerva. Hence the term Golden Number, which de- 
notes the year of the lunar cycle. 

170. The line of the apsides of the moon's orbit re- 
volves from west to east through her whole orbit in about 
nine years. 

If, in any revolution of the moon, we should accu- 
rately mark the place in the heavens where the moon 
comes to its perigee, (which would be known by the 
moon's apparent diameter being then greatest,) we should 
find, that at the next revolution, it would come to its 
perigee at a point a little farther eastward than before, 
and so on at every revolution, until, after nine years, it 
would come to its perigee at nearly the same point as at 
first. This fact is expressed by saying that the perigee 
and of course the apogee, revolves, and that the line 
which joins these two points, or the line of the apsides, 
fdso revolves. 

171. The inequalities of the moon's motions are di- 
vided into periodical and secular. Periodical inequal- 
ities are those which are completed in comparatively 
short periods. Secular inequalities are those which 
are completed only in very long periods, such as cen- 
turies or ages. Hence the corresponding terms peri- 
odical equations and secular equations. As an exam- 
ple of a secular inequality, we may . mention the ac- 
celeration of the moon's mean motion. It is discov- 
ered, that the moon actually revolves around the earth 



170. In what period does the line of the apsides revolve? 
Explain what is meant by this. 



136 THE MOON. 

in less time now than she did in ancient times. The 
difference however is exceedingly small, being only 
about 10" in a century, but increases from century to 
century as the square of the number of centuries. This 
remarkable fact was discovered by Dr. Halley,* In a 
lunar eclipse the moon's longitude differs from that of 
the sun, at the middle of the eclipse, by exactly 180° ; 
and since the sun's longitude at any given time of the 
year is known, if we can learn the day and hour when 
an eclipse occurs, we shall of course know the longitude 
of the sun and moon. Now in the year 721 before the 
Christian era, on a specified day and hour, Ptolemy re- 
cords a lunar eclipse to have happened, and to have been 
observed by the Chaldeans. The moon's longitude, 
therefore, for that time is known ; and as we know the 
mean motions of the moon at present, starting from that 
epoch, and computing, as may easily be done, the place 
which the moon ought to occupy at present at any given 
time, she is found to be actually nearly a degree and a 
half in advance of that place. Moreover, the same con- 
clusion is derived from a comparison of the Chaldean 
observations with those made by an Arabian astronomer 
of the tenth century. 

This phenomenon at first led astronomers to appre- 
hend that the moon encountered a resisting medium, 
which, by destroying at every revolution a small portion 
of her projectile force, would have the effect to bring 
her nearer and nearer to the earth and thus to augment 
her velocity. But in 1786, La Place demonstrated that 



171 . How are the inequalities of the moon's motions divided? 
What are periodical inequalities 1 What are secular inequali- 
ties ? Give an example of a secular inequality. How is it 
known that the moon's motions are accelerated ? What is the 
amount of the acceleration per century ? Will they always 
continue to be accelerated ? 



* Astronomer Royal of Great Britain, and cotemporary with Sir Isaac 
Newton. 



ECLIPSES. 137 

this acceleration is one of the legitimate effects of the 
sun's disturbing force, and is so connected with changes 
in the eccentricity of the earth's orbit, that the moon 
\vill continue to be accelerated while that eccentricity 
diminishes, but when the eccentricity has reached its 
minimum (as it will do after many ages) and begins to 
increase, then the moon's motion will begin to be re- 
tarded, and thus her motions will oscillate forever about 
a mean value. 



CHAPTER V. 

OF ECLIPSES. 

172. An Eclipse of the moon happens when the moon 
in its revolution around the earth, falls into the earth's 
shadow. An Eclipse of the sun happens when the 
moon coming between the earth and the sun, covers 
either a part or the whole of the solar disk. 

The earth and the moon being both opake globular 
bodies exposed to the sun's light, they cast shadows op- 
posite to the sun like any other bodies on which the 
sun shines. Were the sun of the same size with the 
earth and the moon, then the lines drawn touching the 
surface of the sun, and the surface of the earth or moon 
(which lines form the boundaries of the shadow) would 
be parallel to each other, and the shadow would be a 
cylinder infinite in length ; and were the sun less than 
the earth or the moon, the shadow would be an increas- 
ing cone, its narrower end resting on the earth ; but as 



172. When does an eclipse of the moon happen ? When 
does an eclipse of the sun happen ? Were the sun of the same 
size with the earth and moon, how would their shadows be ? 
How if less than these bodies ? How are they in fact? Ex- 
plain by figure 32 

' 12" 



138 



THE MOON. 



the sun is vastly greater than either of these bodies* 
the shadow of each is a cone, whose base rests on the 
body itself, and which comes to a point or vertex at a 
certain distance behind the body. These several cases 
are represented in the following diagrams. 

Fig. 32. 




173. It is found by calculation, that the length of the 
moon's shadow is, on an average, just about sufficient to 
reach to the earth, but the moon is sometimes farther 
from the earth than at others. (Art. 166.) When she is 
nearer than usual, the shadow reaches considerably be- 
yond the surface of the earth. Also the moon as well 
as the earth, is at different distances from the sun at dif- 
ferent times, and its shadow is longest when it is far- 
thest from the sun. Now when both these circumstan- 
ces conspire, that is, when the moon is in her perigee 
and in her aphelion, her shadow extends nearly 15000 
miles beyond the center of the earth, and covers a space 



173. How does the moon's shadow compare with her dis- 
tance from the earth ? When does her shadow extend farthest 
beyond the center of the earth ? What is the greatest breadth 
of her shadow where it falls on the surface of the earth ? What 
is the length of the earth's shadow ? Whenonlycan an eclipse 
of the sun take place ? When only can an eclipse of the moon 
occur ? Explain from figure 33. What is the moon's Pen- 
umbra 1 



ECLIPSES. 



139 



on the surface of the earth 170 miles broad. The 
earth's shadow is towards a million of miles in length, 
and more than three and a half times as long as the dis- 
tance from the earth to the moon ; and it is also at the 
distance of the moon three times as broad as the moon 
itself. An eclipse of the sun can take place only at new 
moon, when the sun and moon meet in the same part of 
the heavens, for then only can the moon come between 
us and the sun ; and an eclipse of the moon can occur 
only when the sun and moon are in opposite parts of 
the heavens, or at full moon, for then only can the moon 
fall into the shadow of the earth. 

The nature of eclipses will be clearly understood from 
the following representation. This figure exhibits the 

Fig. 33. 





relative position of the sun, the earth, and the moon, 
both in a solar and in a lunar eclipse. It is evident from 
the figure, that if a spectator were situated where the 
moon's shadow strikes the earth, the moon would cut oft* 
from him the view of the sun, or the sun would be to- 
tally eclipsed. Or, if he were within a certain distance 
of the shadow on either side, the moon would be partly 
between him and the sun, and would intercept from 
him more or less of the sun's light, according as he was 
nearer to the shadow or farther from it. If he were at 
c, or a, he would just see the moon entering upon the 



140 THE MOON. 

sun's disk ; if he were nearer the shadow than either of 
these points, he would have a portion of the sun's light 
cut off from his view, and the moment he entered the 
shadow itself, he would lose sight of the sun. To all 
places between c or d and the shadow, the sun would 
cast a partial shadow of the moon, growing deeper and 
deeper as it approached the true shadow. This partial 
shadow is called the moon's Penumbra. In like man- 
ner, as the moon approaches the earth's shadow in a lu- 
nar eclipse, as soon as she arrives at a, the earth begins 
to intercept from her a portion of the sun's light, or she 
falls into the earth's penumbra. She continues to lose 
more and more of the sun's light as she draws near to 
the shadow, and hence her disk becomes gradually ob- 
scured, until it enters the shadow, where the sun's light 
is entirely lost. 

174. As the sun and earth are both situated in the 
plane of the ecliptic, if the moon also revolved around 
the earth in this plane, we should have a solar eclipse at 
every new moon, and a lunar eclipse at every full 
moon ; for in the former case the moon would come di- 
rectly between us and the sun, and in the latter case, 
the earth would come directly between the sun and the 
moon. But the moon's path is inclined to the ecliptic 
about 5°, and the center of the moon may be all this 
distance from the center of the sun, at new moon, and 
the same distance from the center of the earth's shadow 
at full moon. It is true the moon extends across her 
path, one half her breadth lying on each side of it, and 
the sun likewise reaches from the ecliptic a distance 
equal to half his breadth. But these luminaries to- 
gether make but little more than a degree, and conse- 
quently their two semi-diameters would occupy only 



174. Why do we not have a solar eclipse every new moon, 
and a lunar eclipse every full moon ? Explain how eclipses 
occur only when the sun is near one of the moon's nodes, by 
fiffure 34. 



ECLIPSES. 



141 



about half a degree of the five degrees from one orbit 
to the other. Also the earth's shadow where the moon 
crosses it extends from the ecliptic less than three 
fourths of a degree, so that the semi-diameter of the 
moon and of the earth's shadow, would together reach 
but little way across the space that may in certain cases 
separate the two luminaries from each other when they 
are in opposition. Thus suppose we could take hold 
of the circle in the figure that represents the moon's 
orbit, (Fig. 31,) and lift the moon up five degrees above 
the plane of the paper, it is evident that the moon 
as seen from the earth, would appear in the heavens 
five degreess above the sun, and of course would cut off 
none of his light, and that the moon at the full would 
pass the shadow of the earth five degrees below it, and 
would suffer no eclipse. But in the course of the sun's 
apparent revolution around the earth once a year, he is 
successively in every part of the ecliptic ; consequently, 
the conjunctions and oppositions of the sun and moon 
may occur at any part of the ecliptic, and of course at 
the two points where the moon's orbit crosses the eclip- 
tic, that is, at the nodes, for the sun must necessarily 
come to each of these nodes once a year. If then the 
moon overtakes the sun just as she is crossing his path, 

Fig. 34. 




she will hide more or less of his disk from us. Since, 
also, the earth's shadow is always directly opposite to 
the sun, if the sun is at one of the nodes, the shadow 



142 THE MOON. 

must extend in the direction of the other node, so as to 
lie directly across the moon's path, and if the moon over- 
takes it there, she will pass through it and be eclipsed. 
Thus in figure 34, let BN represent the sun's path, and 
AN the moon's, N being the place of the node ; then it is 
evident that if the two luminaries at new moon be so 
far from the node, that the distance between their centers 
is greater than their semi-diameters, no eclipse can hap- 
pen ; but if that distance is less than this sum as at 
E, F, then an eclipse will take place, but if the position 
De as at C, D, the two bodies will just touch one another. 
If A denote the earth's shadow instead of the sun, the 
same illustration will apply to an eclipse of the moon. 

175. Since bodies are defined to be in conjunction 
when they are in the same part of the heavens, and to 
be in opposition when they are in opposite parts of the 
heavens, it may not appear how the sun and moon can 
be in conjunction as at A and B, when they are still at 
some distance from each other. But it must be recol- 
lected that bodies are in conjunction when they have the 
same longitude, in which case they are both situated in 
the same great circle perpendicular to the ecliptic, that 
is, in the same secondary to the ecliptic. One of the 
bodies may be much farther from the ecliptic than the 
other ; still, if the same secondary to the ecliptic passes 
through them both, they will be in conjunction or oppo- 
sition. 

176. In a total eclipse of the moon, its disk is still 
visible, shining with a dull red light. This light cannot 
be derived directly from the sun, since the view of the 
sun is completely hidden from the moon ; nor by reflex- 
ion from the earth, since the illuminated side of the 



175. Is it necessary for two bodies to be precisely together 
in order to be in conjunction ? 

176. Why is the disk of the moon still visible in a total 
eclipse of the moon ? 



ECLIPSES. 143 

earth is wholly turned from the moon ; but it is owing 
to refraction from the earth's atmosphere, by which a 
few scattered rays of the sun are bent round into the 
earth's shadow and conveyed to the moon, sufficient in 
number to afford the feeble light in question. 

177. It is impossible fully to understand the method 
of calculating eclipses, without a knowledge of trigo- 
nometry ; still it is not difficult to form some general no- 
tion of the process. It may be readily conceived that, 
by long continued observations on the sun and moon, 
the exact places which they will occupy in the heavens 
at any future times, may be forseen and laid down in 
tables of the sun and moon's motions ; that we may thus 
ascertain by inspecting the tables the exact instant when 
these two bodies will appear together in the heavens, or 
be in conjunction, and when they will be 180° apart, 
or in opposition. Moreover, since the exact place of the 
moon's node among the stars at any particular time is 
known to astronomers, it cannot be difficult to determine 
when the new or full moon occurs in the same part of 
the heavens as that where the node is projected as seen 
from the earth. In short, as astronomers can easily de- 
termine what will be the relative position of the sun, 
the moon, and the moon's nodes for any given time, 
they can tell when these luminaries will meet so near 
the node as to produce an eclipse of the sun, or when 
they will be in opposition so near the node as to produce 
an eclipse of the moon. 

178. Let us endeavor to form a just conception of the 
manner in which these three bodies, the sun, the earth, 
and the moon, are situated with respect to each other at 
the time of a solar eclipse. First, suppose the conjunction 
to take place at. the node. Then the straight line which 
connects the center of the sun and the earth, also passes 



177. What science must be known in order fully to under- 
stand the mode of calculating eclipses ? Explain the general 
principles of the calculation. 



144 THE MOON. 

through the center of the moon, and coincides with the 
axis of its shadow ; and, since the earth is bisected by 
the plane of the ecliptic, the shadow would traverse the 
earth in the direction of the terrestrial ecliptic, from 
west to east, passing over the middle regions of the 
earth. Here the diurnal motion of the earth being in 
the same direction with the shadow, but with a less ve- 
locity, the shadow will appear to move with a speed 
equal only to the difference between the two. Secondly, 
suppose the moon is on the north side of the ecliptic at 
the time of conjunction, and moving towards her de- 
scending node, and that the conjunction takes place 
as far from the node as an eclipse can happen. The 
shadow will not fall in the plane of the ecliptic, but 
a little northward of it, so as just to graze the earth 
near the pole of the ecliptic. The nearer the conjunc- 
tion comes to the node, the farther the shadow will fall 
from the pole of the ecliptic towards the equatorial re- 
gions. 

179. The leading particulars respecting an eclipse 
of the sun, are ascertained very nearly like those of a 
lunar eclipse. The shadow of the moon travels over a 
portion of the earth, as the shadow of a small cloud, seen 
from an eminence in a clear day, rides along over hills 
and plains. Let us imagine ourselves standing on the 
moon ; then we shall see the earth partially eclipsed by 
the shadow of the moon, in the same manner as we 
now see the moon eclipsed by the earth's shadow. 

But, although the general characters of a solar eclipse 
might be investigated on these principles, so far as re- 
spects the earth at large, yet as the appearances of the 
same eclipse of the sun are very different at different 
places on the earth's surface, it is necessary to calculate 



1 78. Explain the relative position of the sun, the earth, and 
the moon, in a solar eclipse. Explain the circumstances when 
the conjunction takes place at the node, and when it occurs at 
a distance from the node. 



^ 



ECLIPSES. 145 

its peculiar aspects for each place separately, a circum- 
stance which makes the calculation of a solar eclipse 
much more complicated and tedious than of an eclipse 
of the moon. The moon, when she enters the shadow 
of the earth, is deprived of the light of the part immer- 
sed, and that part appears black alike to all places where 
the moon is above the horizon. But it is not so with a 
solar eclipse. We do not see this by the shadow cast 
on the earth, as we should do if we stood on the moon, 
but by the interposition of the moon between us and the 
sun ; and the sun may be hidden from one observer 
while he is in full view of another only a few miles dis- 
tant. Thus, a small insulated cloud sailing in a clear 
sky, will, for a few moments, hide the sun from us, and 
from a certain space near us, while all the region around 
is illuminated. 

We have compared the motion of the moon's shadow 
over the surface of the earth to that of a cloud ; but its 
velocity is incomparably greater. The mean motion of 
the moon around the earth is about 33' per hour ; but 
33' of the moon's orbit is 2280 miles, and the shadow 
moves of course at the same rate, or 2280 miles per 
hour, traversing the entire disk of the earth in less than 
four hours. 

180. The diameter of the moon's shadow where it 
eclipses the earth can never exceed 170 miles, and com- 
monly falls much short of that ; and the greatest por- 
tion of the earth's surface ever covered by the moon's 
penumbra is about 4393 miles. 

181. The apparent diameter of the moon is sometimes 
larger than that of the sun, sometimes smaller, and 



179. Hcnr are theleadingparticulars of an eclipse of the sun 
ascertained 1 How illustrated by the motion of a cloud ? In 
what respects does the calculation of a solar differ from that of 
a lunar eclipse ? How does the shadow of the moon compare 
with that of a cloud in velocity ? 

13 



146 



THE MOON. 



sometimes exactly equal to it. Suppose an observer 
placed on the right line which joins the centers of the 
sun and moon ; if the apparent diameter of the moon is 
greater than that of the sun, the eclipse will be total. If 
the two diameters are equal, the moon's shadow jusl 
reaches the earth, and the sun is hidden but for a mo- 
ment from the view of spectators situated in the line 
which the vertex of the shadow describes on the surface 
of the earth. But if, as happens when the moon comes 
to her conjunction in that part of her orbit which is to- 
wards her apogee, the moon's diameter is less than the 
sun's, then the observer will see a ring of the sun en- 
circling the moon, constituting an Annular Eclipse, as in 
figure 35. 

Fig. 35. 




180. What cannot the diameter of the moon's shadow 
where it eclipses the earth, exceed ? What is the greatest 
portion of the earth's surface ever covered by the moon's pe- 
numbra ? 

181. How does the moon's apparent diameter compare with 
the sun's 1 When will the eclipse be total, and when annular ? 



ECLIPSES. 147 

182. Eclipses of the sun are modified by the eleva- 
tion of the moon above the horizon, since its apparent 
diameter is augmented as its altitude is increased. This 
affect, combined with that of parallax, may so increase 
or diminish the apparent distance between the centers of 
the sun and moon, that from this cause alone, of two 
observers at a distance from each other, one might see 
on eclipse which was not visible to the other. If the 
horizontal diameter of the moon differs but little from 
the apparent diameter of the sun, the case might occur 
where the eclipse would be annular over the places 
where it was observed morning and evening, but total 
where it was observed at mid-day. 

The earth in its diurnal revolution and the moons 
shadow both move from west to east, but the shadow 
moves faster than the earth ; hence the moon overtakes 
the sun on its western limb and crosses it from west to 
east. The excess of the apparent diameter of the moon 
above that of the sun in a total eclipse is so small, that 
total darkness seldom continues longer than four minutes, 
and can never continue so long as eight minuutes. An 
annular eclipse may last 12m. 24s. 

183. Eclipses of the sun are more frequent than those 
of the moon. Yet lunar eclipses being visible to every 
part of the terrestrial hemisphere opposite to the sun, 
while those of the sun are visible only to the small por- 
tion of the hemisphere on which the moon's shadow 
falls, it happens that for any particular place on the 
earth, lunar eclipses are more frequently visible than 
solar. In any year, the number of eclipses of both lu- 



182. Ifow are eclipses of the sun modified by the elevation 
of the moon above the horizon ? How might the same eclipse 
appear total to one observer and annular to another ? How 
long can total darkness continue in a solar eclipse 1 How long 
may an annular eclipse last ? 

183. Which are most frequent, solar or lunar eclipses ? Why 
does an eclipse of the moon sometimes happen at the next full 
moon after an eclipse of the sun ? 



148 REVOLUTIONS. 

minaries cannot be less than two nor more than seven : 
the most usual number is four, and it is very rare to 
have more than six. A total eclipse of the moon fre- 
quently happens at the next full moon after an eclipse 
of the sun. For since, in an eclipse of the sun, the sun 
is at or near one of the moon's nodes, the earth's shadow 
must be at or near the other node, and may not have 
passed far from the node before the moon overtakes it. 

184. In total eclipses of the sun, there has sometimes 
been observed a remarkable radiation of light from the 
margin of the sun. This has been ascribed to an illu- 
mination of the solar atmosphere, but it is with more 
probability owing to the zodiacal light, which at that 
time is projected around the sun, and which is of such 
dimensions as to extend far beyond the solar orb.* 

A total eclipse of the sun is one of the most sublime 
and impressive phenomena of nature. Among barbarous 
tribes it is ever contemplated with fear and astonish- 
ment, while among cultivated nations it is recognized, 
from the exactness with which the time of occurrence 
and the various appearances answer to the prediction, as 
affording one of the proudest triumphs of astronomy. 
By astronomers themselves it is of course viewed with 
the highest interest, not only as verifying their calcula- 
tions, but as contributing to establish beyond all doubt 
the certainty of those grand laws, the truth of which is 
involved in the result. During the eclipse of June, 
1806, which was one of the most remarkable on record, 
the time of total darkness, as seen by the author of this 
work, was about mid-day. The sky was entirely eloud- 



1 84. How is the radiation of light around the margin of the 
sun in a total eclipse of the sun, accounted for ? How have 
eclipses of the sun been regarded among barbarous tribes ? 
How among civilized nations 1 How by astronomers ? Give 
some account of the great eclipse of 1806. 

* See an excellent description and delineation of this appearance as 
it was exhibited in the eclipse of 1806, in the Transactions of the Al- 
bany Institute, by the late Chancellor De Witt. 



ECLIPSES 149 

less, but as the period of total obscuration approached, a 
gloom pervaded all nature. When the sun was wholly 
lost sight of, planets and stars came into view ; a fearful 
pall hung upon the sky, unlike both to night and to 
twilight ; and, the temperature of the air rapidly de- 
clining, a sudden chill came over the earth. Even the 
animal tribes exhibited tokens of fear and agitation. 

185. The word Eclipse is derived from a Greek word, 
(exleufjig,) which signifies to fail, to faint, or swoon 
away, since the moon at the period of her greatest 
brightness falling into the shadow of the earth, was im- 
agined by the ancients to sicken and swoon, as if she 
were going to die. By some very ancient nations she 
was supposed at such times to be in pain, and hence 
lunar eclipses were called the labors of the moon, (lunae 
labores ;) and, in order to relieve her fancied distress, they 
lifted torches high in the atmosphere, blew horns and 
trumpets, beat upon brazen vessels, and even, after the 
eclipse was over, they offered sacrifices to the moon. 
The opinion also extensively prevailed, that it was in 
the power of witches, by their spells and charms, not 
only to darken the moon, but to bring her down from 
her orbit, and to compel her to shed her baleful influences 
upon the earth. In a solar eclipse also, especially when 
total, the sun was supposed to turn away his face in ab- 
horrence of some atrocious crime, that either had been 
perpetrated or was about to be perpetrated, and to 
threaten mankind with everlasting night, and the de- 
struction of the world. 

The Chinese, who from a very high period of anti- 
quity have been great observers of eclipses, although 
they did not take much notice of those of the moon, re- 
garded eclipses of the sun in general as unfortunate, but 
especially such as occurred on the first day of the year. 



185. From what is the word eclipse derived 1 What ideas 
had certain ancient nations respecting eclipses ? With what 
ceremonies did they observe them ? How were eclipses re- 
garded among the Chinese 1 

' 13* 



150 THE MOON. 

These were thought to forbode the greatest calamities 
to the emperor, who on such occasions did not receive 
the usual compliments of the season. When an eclipse 
of the sun was expected from the predictions of their as- 
tronomers, they made great preparation at court for ob- 
serving it ; and as soon as it commenced, a blind man 
beat a drum and a great concourse assembled, and the 
Mandarins, or nobility, appeared in state. 

186. From 1831 to 1838, was a period distinguished 
for great eclipses of the sun, in which time there were no 
less than five, of the most remarkable character. The 
next total eclipse of the sun, visible in the United States, 
will occur on the 7th of August, 1869. 



CHAPTER VI. 

OF LONGITUDE. TIDES. 

187. As eclipses of the sun afford one of the most 
approved methods of finding the longitude of places, our 
attention is naturally turned next towards that subject. 

The ancients studied astronomy in order that they 
might read their destinies in the stars : the moderns that 
they may securely navigate the ocean. A large portion 
of the refined labors of modern astronomy, has been di- 
rected towards perfecting the astronomical tables with 
the view of finding the longitude at sea, — an object 
manifestly worthy of the highest efforts of science, con- 
sidering the vast amount of property and of human life 
involved in navigation. 

188. The difference of longitude between two places, 
may be found by any method by which we can ascertain 



1S6. What recent period has abounded with great eclipses 
of the sun ? When will the next total eclipse of the sun occur ? 

187. For what purpose did the ancients study astronomy ? 
For what purpose do the moderns study it ? 



LONGITUDE. 151 

the difference of their local times, at the same instant of 
absolute time. 

As the earth turns on its axis from west to east, any 
place that lies eastward of another will come sooner un- 
der the sun, or will have the sun earlier on the meridian, 
and consequently, in respect to the hour of the day, will 
be in advance of the other at the rate of one hour for 
every 15°, or four minutes of time for each degree. Thus, 
to a place 15° east of Greenwich, it is 1 o'clock, P. M. 
when it is noon at Greenwich; and to a place 15° west 
of that meridian, it is 11 o'clock, A. M. at the same in- 
stant. Hence the difference of time at any two places, 
indicates their difference of longitude. 

189. The easiest method of finding the longitude is 
by means of an accurate time piece, or chronometer. Let 
us set out from London with a chronometer accurately 
adjusted to Greenwich time, and travel eastward to a 
certain place, where the time is accurately kept, or may 
be ascertained by observation. We find, for example, 
that it is 1 o'clock by our chronometer, when it is 2 
o'clock and 30 minutes at the place of observation. 
Hence the longitude is 15 x 1.5=22J° E. Had we trav- 
elled westward until our chronometer was an hour and 
a half in advance of the time at the place of observa- 
tion, (that is, so much later in the day,) our longitude 
would have been 22^° W. But it would not be neces- 
sary to repair to London in order to set our chronometer 
to Greenwich time. This might be done at any obser- 
vatory, or any place whose longitude has been accu- 



188. How may the difference of longitude between two pla- 
ces be found ? How many degrees of longitude, correspond to 
one hour in time ? How many minutes to one degree ? 

189. Explain the method of finding the longitude by the 
chronometer. To what time is it set l How do we ascertain 
die longitude of a place by it 1 Would it be necessary to re- 
pair to Greenwich to regulate our chronometer ? What is said 
of the accuracy of some chronometers ? Why is not this 
method adapted to general use ? 



152 THE MOON. 

rately determined. For example, the time at New York 
is 4h. 56m. 4s. 5 behind that of Greenwich. If, there- 
fore, we set our chronometer so much before the true 
time at New York, it will indicate the time at Green- 
wich. Moreover, on arriving at different places any 
where on the earth, whose longitude is accurately known, 
we may learn whether our chronometer keeps accurate 
time or not, and if not, the amount of its error. Chro- 
nometers have been constructed of such an astonishing 
degree of accuracy, as to deviate but a few seconds in a 
voyage from London to Baffin's Bay and back, during an 
absence of several years. But chronometers which are 
sufficiently accurate to be depended on for long voya- 
ges, are too expensive for general use, and the means of 
verifying their accuracy are not sufficiently easy. More- 
over, chronometers, by being transported from one place 
to another, change their daily rate, or depart from that 
mean rate which they preserve at a fixed station, A 
chronometer, therefore, cannot be relied on for determin- 
ing the longitudes of places where the greatest degree of 
accuracy is required, especially where the instrument is 
conveyed over land, although the uncertainty attendant 
on one instrument may be nearly obviated by employing 
several and taking their mean results. 

190. Eclipses of the sun and moon are sometimes 
used for determining the longitude. The exact instant 
of immersion or of emersion, or any other definite mo- 
ment of the eclipse which presents itself to two distant 
observers, affords the means of comparing their difference 
of time, and hence of determining their difference of 
longitude. Since the entrance of the moon into the 
earth's shadow, in a lunar eclipse, is seen at the same 
instant of absolute time at all places where the eclipse 
is visible, this observation would be a very suitable one 
for finding the longitude were it not that, on account of 



190. Explain how to find the longitude by eclipses of the sun 
and moon. What objections are there to this method, both in 
lunar and solar eclipses ? 



LONGITUDE. 153 

the increasing darkness of the penumbra near the boun- 
daries of the shadow, it is difficult to determine the pre- 
cise instant when the moon enters the shadow. By 
taking observations on the immersions of known spots 
on the lunar disk, a mean result may be obtained which 
will give the longitude with tolerable accuracy. In an 
eclipse of the sun, the instants of immersion and emer- 
sion may be observed with greater accuracy, although, 
since these do not take place at the same instant of ab- 
solute time, the calculation of the longitude from obser- 
vations on a solar eclipse are complicated and laborious. 

191. The lunar method of finding the longitude, at 
sea, is in many respects preferable to every other. It 
consists in measuring (with a sextant) the angular dis- 
tance between the moon and the sun, or between the 
moon and a star, and then turning to the Nautical Alma- 
nac,* and finding what time it was at Greenwich when 
that distance was the same. The moon moves so rap- 
idly, that this distance will not be the same except at 
very nearly the same instant of absolute time. For ex- 
ample, at 9 o'clock, A. M., at a certain place, we find the 
angular distance of the moon and the sun to be 72° ; 
and, on looking into the Nautical Almanac, we find that 
the time when this distance was the same for the me- 
ridian of Greenwich was 1 o'clock, P. M. ; hence we 
infer that the longitude of the place is four hours, or 00° 
west. 



191. Explain the lunar method of finding the longitude. 
What measurements are made ? How do we find the corres- 
ponding time at Greenwich ? 



* The Nautical Almanac, is a bock published annually by the British 
Board of Longitude, containing various tables and astronomical infor- 
mation for the use of navigators. The American Almanac also con- 
tains a variety of astronomical information, peculiarly interesting to the 
people of the United States, in connexion with a vast amount of 
statistical matter. It is well deserving of a place in the library of the 
student. 



154 THE MOON. 

The Nautical Almanac contains the true angular dis- 
tance of the moon from the sun, from the four large 
planets, (Venus, Mars, Jupiter, and Saturn,) and from 
nine bright fixed stars, for the beginning of every third 
hour of mean time for the meridian of Greenwich ; and 
the mean time corresponding to any intermediate hour, 
may be found by proportional parts.* 

192. It would be a very simple operation to determine 
the longitude by Lunar Distances, if the process as de- 
scribed in the preceding article were all that is neces- 
sary ; but the various circumstances of parallax, refrac- 
tion, and dip of the horizon, would differ more or less at 
the two places, even were the bodies, whose distances 
were taken, in view from both, which is not necessarily 
the case. The observations, therefore, require to be 
reduced to the center of the earth, being cleared of the 
effects of parallax and refraction. Hence, three obser- 
vers are necessary in order to take a lunar distance in 
the most exact manner, viz. two to measure the altitudes 
of the two bodies respectively, at the same time that 
the third takes the angular distance between them. 
The altitudes of the two luminaries at the time of ob- 
servation must be known, in order to estimate the effects 
of parallax and refraction. 

193. Although the lunar method of finding the longi- 
tude at sea has many advantages over the other meth- 
ods in use, yet it also has its disadvantages. One is, the 
great exactness requisite in observing the distance of 
the moon from the sun or star, as a small error in the 
distance makes a considerable error in the longitude. 
The moon moves at the rate of about a degree in two 



192. What difficulties are there in this method ? Why are 
three observers necessary ? 

193. What are the objections to this method ? What is the 
error of the best tables now in use 1 

* See Bowditch's Navigator, Tenth Ed. p. 226. 



LONGITUDE. 155 

hours, or one minute of space in two minutes of time. 
Therefore, if we make an error of one minute in ob- 
serving the distance, we make an error of two minutes 
in time, or 30 miles of longitude at the equator. A sin- 
gle observation with the best sextant, may be liable to 
an error of more than half a minute ; but the accuracy 
of the result may be much increased by a mean of sev- 
eral observations taken to the east and west of the moon. 
The imperfection of the lunar tables was until recently 
considered as an objection to this method. Until within a 
few years, the best lunar tables were frequently errone- 
ous to the amount of one minute, occasioning an error 
of 30 miles. The error of the best tables now m use 
will rarely exceed 7 or 8 seconds. 

TIDES. 

194. The tides are an alternate rising and falling of 
the waters of the ocean, at regular intervals. They have 
a maximum and a minimum twice a day, twice a month, 
and twice a year. Of the daily tide, the maximum is 
called High tide, and the minimum Low tide. The 
maximum for the month is called Spring tide, and the 
minimum Neap tide. The rising of the tide is called 
Flood and its falling Ebb tide. 

Similar tides, whether high or low, occur on opposite 
sides of the earth at once. Thus at the same time that it 
is high tide at any given place, it is also high tide on the 
inferior meridian, and the same is true of the low tides. 

The interval between two successive high tides is 
12h. 25m.; or, if the same tide be considered as return- 
ing to the meridian, after having gone around the globe, 



194. What are the tides 1 When have they a maximum and 
a minimum ? Define the terms High and Low, Spring and 
Neap, Flood and Ebb tides. What two tides occur at the same 
time 1 What is the interval between two successive high tides ? 
How rmieh later is the tide of to-day than the same tide of 
yesterday ? What is the average height of the tide for the 
whole globe ? To what extreme height does it sometimes rise ? 
Have inland lakes and seas any tides ? 



156 /HE MOON 

its return is about 50 minutes later than it occurred on 
the preceding day. In this respect, as well as in various 
others, it corresponds very nearly to the motions of the 
moon. 

The average height for the whole globe is about 2^ 
feet ; or, if the earth were covered uniformly with a 
stratum of water, the difference between the two diam- 
eters of the oval would be 5 feet, or more exactly 5 feet 
and 8 inches ; but its actual height at various places is 
very various, sometimes rising to 60 or 70 feet, and 
sometimes being scarcely perceptible. At the same 
place also, the phenomena of the tides are very different 
at different times. 

Inland lakes and seas, even those of the largest class, 
as Lake Superior, or the Caspian, have no perceptible 
tide. 

195. Tides are caused by the unequal attraction of 
the sun and moon upon different parts of the earth. 

Suppose the projectile force by which the earth is car- 
ried forward in her orbit, to be suspended, and the earth 
to fall towards one of these bodies, the moon, for exam- 
ple, in consequence of their mutual attraction. Then, 
if all parts of the earth fell equally towards the moon, 
no derangement of its different parts would result, any 
more than of the particles of a drop of water in its de- 
scent to the ground. But if one part fell faster than an- 
other, the different portions would evidently be separa- 
ted from each other. Now this is precisely what takes 
place with respect to the earth in its fall towards the 
moon. The portions of the earth in the hemisphere 
next to the moon, on account of being nearer to the 
center of attraction, fall faster than those in the oppo- 
site hemisphere, and consequently leave them behind. 
The solid earth, on account of its cohesion, cannot obey 



195. State the cause of the tides. What would be the con- 
sequence were the earth abandoned to the force exerted by 
the moon alone ? 



TIDES. 



157 



this impulse, since all its different portions constitute 
one mass, which is acted on in the same manner as 
though it were all collected in the center ; but the wa- 
ters on the surface, moving freely under this impulse, 
endeavor to desert the solid mass and fall towards the 
moon. For a similar reason the waters in the opposite 
hemisphere falling less towards the moon than the solid 
earth are left behind, or appear to rise from the center 
of the earth. 

196. Let DEFG (Fig. 36,) represent the globe ; and, 
for the sake of illustrating the principle, we will sup- 
pose the waters entirely to cover the globe at a uniform 
depth. Let defg represent the solid globe, and the cir- 




cular ring exterior to it, the covering of waters. Let C 
be the center of gravity of the solid mass, A that of the 
hemisphere next to the moon, (for the center of gravity 
of a ring is within the ring,) and B that of the remoter 
hemisphere. Now the force of attraction exerted by 
the moon, acts in the same manner as though the solid 
mass were all concentrated in C, and the waters of each 
hemisphere at A and B respectively ; and (the moon be- 



196. Explain the tides upon the doctrine of the center of 
gravity. Where would the tide-wave always be seen were it 
not for impediments ? What are these ? 

14 



158 THE MOON. 

ing supposed above E) it is evident that A will tend to 
leave C, and C to leave B behind. The same must evi- 
dently be true of the respective portions of matter, of 
which these points are the centers of gravity. The wa- 
ters of the globe will thus be reduced to an oval shape, 
being elongated in the direction of that meridian which 
is under the moon, and flattened in the intermediate 
parts, and most of all at points ninety degrees distant 
from that meridian. 

Were it not, therefore, for impediments which prevent 
the force from producing its full effects, we might expect 
to see the great tide-wave, as the elevated crest is called, 
always directly beneath the moon, attending it regularly 
around the globe. But the inertia of the waters pre- 
vents their instantly obeying the moon's attraction, and 
the friction of the waters on the bottom of the ocean, 
still farther retards its progress. It is not therefore until 
several hours (differing at different places) after the 
moon has passed the meridian of a place, that it is high 
tide at that place. 

197. The sun has a similar action to the moon, but 
only one third as great. On account of the great mass 
of the sun compared with that of the moon, we might 
suppose that his action in raising the tides would be 
greater than that of the moon ; but the nearness of the 
moon to the earth more than compensates for the sun's 
greater quantity of matter. Let us, however, form a just 
conception of the advantage which the moon derives 
from her proximity. It is not that her actual amount of 
attraction is thus rendered greater than that of the sun ; 
but it is that her attraction for the different parts of the 
earth is very unequal, while that of the sun is nearly 
uniform. It is the inequality of this action, and not the 
absolute force, that produces the tides. The diameter of 
the earth is -^ of the distance of the moon, while it is 
less than -3-0^00 °f tne distance of the sun. 



197. Explain the action of the sun in raising the tide ? Why 
is its efFect less than that of the moon ? 



TIDES. 159 

198. Having now learned the general cause of the 
tides, we will next attend to the explanation of -particu- 
lar phenomena. 

The Spring tides, or those which rise to an unusual 
height twice a month, are produced by the sun and 
moon's acting together ; and the Neap tides, or those 
which are unusually low twice a month, are produced 
by the sun and moon's acting in opposition to each 
other. The Spring tides occur at the syzigies : the 
Neap tides at the quadratures. At the time of new moon, 
the sun and moon both being on the same side of the 
earth, and acting upon it in the same line, their actions 
conspire, and the sun may be considered as adding so 
much to the force of the moon. We have already ex- 
plained how the moon contributes to raise a tide on the 
opposite side of the earth. But the sun as well as the 
moon raises its own tide-wave, which, at new moon, 
coincides with the lunar tide-wave. At full moon, also, 
the two luminaries conspire in the same way to raise 
the tide ; for we must recollect that each body contri- 
butes to raise the tide on the opposite side of the earth 
as well as on the side nearest to it. At both the con- 
junctions and oppositions, therefore, that is, at the syzi- 
gies, we have unusually high tides. But here also the 
maximum effect is not at the moment of the syzigies, 
but 36 hours afterwards. 

At the quadratures, the solar wave is lowest where the 
lunar wave is highest ; hence the low tide produced by 
the sun is subtracted from high water and produces the 
Neap tides. Moreover, at the quadratures the solar 
wave is highest where the lunar wave is lowest, and 
hence is to be added to the height of low water at the 
time of Neap tides. Therefore the difference between 
high and low water is only about half as great at Neap 
tide as at Spring tide. 



198. What is the cause of the Springtides 1 Also of the 
Neap.tides? How long after the syzigies does the highest 
tide occur 1 



160 



THE MOON 



199. The variations of distance in the sun are not 
great enough to influence the tides very materially, but 
the variations in the moon's distance have a striking 
effect. The tides which happen when the moon is in 
perigee, are considerably greater than when she is in 
apogee ; and if she happens to be in perigee at the time 
of the syzigies, the Spring tide is unusually high. 
When this happens at the equinoxes, the highest tides 
of the year are produced. 

200. The declinations of the sun and moon have a 
considerable influence on the height of the tide. When 
the moon, for example, has no declination, or is in the 

Fig. 37. 




equator, as in figure 37,* the two tides will be exactly 
equal on opposite sides of the meridian in the same 
parallel. Thus a place in the parallel TT' will have 



199. How do the variations in the moon's distance from the 
earth affect the tides ? How are the tides when the moon is in 
perigee ? How when she in apogee ? When are the highest 
tides of the year produced 1 



* Diagrams like these are apt to mislead the learner, by exhibiting the 
protuberance occasioned by the tides as much greater than the reality. 
We must recollect that it amounts, at the highest, to only a very few 
feet in eight thousand miles. Were the diagram, therefore, drawn in 
just proportions, the alteration of figure produced by the tides would 
be wholly insensible. 



TIDES. 



161 



the height of one tide T2 and the other tide T'3. 
The tides are in this case greatest at the equator, and 
diminish gradually to the poles, where it will be low 
water during the whole day. When the moon is 
on the north side of the equator, as in figure 38, at 
her greatest northern declination, a place describing 
the parallel TT' will have T'3 for the height of the 

Fig. 38. 




tide when the moon is on the superior meridian, and T2 
for the height at the same time on the inferior me- 
ridian. Therefore, all places north of the equator will 
have the highest tide when the moon is above the hor- 
izon, and the lowest when she is below it ; the differ- 
ence of the tides diminishing towards the equator, where 
they are equal. In like manner, (the moon being still 
at M, Fig. 38, that is, having northern declination,) 
places south of the equator have the highest tides when 
the moon is below the horizon, and the lowest when she 
is above it. The circumstances are all reversed when 
the moon is south of the equator. 

201. The motion of the tide- wave, it should be re- 
marked, is not a. progressive motion, but a mere undula- 
tion, and is to be carefully distinguished from the cur- 



200 Explain the effect of the declinations of the sun and 
moon upon the tides. How will the upper and lower tides cor- 
respond when the moon is in the equator 1 How when the 
moon is north of the equator ? Explain by figures 37, 38 
, 14 * 



162 THE MOON. 

rents to which it gives rise. If the ocean completely 
covered the earth, the sun and moon being in the equa- 
tor, the tide-wave would travel at the same rate as the 
earth on its axis. Indeed, the correct way of conceiv- 
ing of the tide- wave, is to consider the moon at rest, 
and the earth in its rotation from west to east, as bringing 
successive portions of water under the moon, which 
portions being elevated successively at the same rate as 
the earth revolves on its axis, have a relative motion 
westward in the same degree. 

202. The tides of rivers, narrow bays, and shores 

for from the main body of the ocean, are not produced 

in those places by the direct action of the sun and moon, 

but are subordinate waves propagated from the great 

tide-wave. 

Lines drawn through all the adjacent parts of any 
tract of water, which have high water at the same time, 
are called cotidal lines. We may, for instance, draw a 
line through all places in the Atlantic Ocean which 
have high tide in a given day at 1 o'clock, and another 
through all places which have high tide at 2 o'clock. 
The cotidal line for any hour may be considered as rep- 
resenting the summit or ridge of the tide-wave at that 
time ; and could the spectator, detached from the earth, 
perceive the summit of the wave, he would see it travel- 
ing round the earth in the open ocean once in twenty- 
four hours, followed by another twelve hours distant, 
and both sending branches into rivers, bays, and other 
openings into the main land. These latter are called 
Derivative tides, while those raised directly by the ac- 
tion of the sun and moon, are called Primitive tides. 



201. Is the motion of the tide-wave progressive? if the 
ocean completely covered the earth and the sun and moon were 
in the equator, how would the tide-wave travel 1 What is the 
most correct way of conceiving of the tide-wave ? 

202. How are the tides of rivers, &c. produced? Define 
cotidal lines. What does the cotidal line for any hour repre- 
sent ? Distinguish between Primitive and Derivative tides. 



TIDES 



163 



203. The velocity with which the wave moves, will 
depend on various circumstances, but principally on the 
depth, and probably on the regularity of the channel. 
If the depth be nearly uniform, the cotidal lines will be 
nearly straight and parallel. But if some parts of the 
channel are deep while others are shallow, the tide will 
be detained by the greater friction of the shallow places, 
and the cotidal lines will be irregular. The direction 
also of the derivative tide, may be totally different from 
that of the primative. Thus, (Fig, 39,) if the great 

Fig. 39. 




tide-wave, moving from east to west, be represented by 
the lines 1, 2, 3, 4, the derivative tide which is propa- 
gated up a river or bay, will be represented by the co- 
tidal lines 3. 4, 5, 6, 7. Advancing faster in the channel 
than next the bank, the tides will lag behind towards 
the shores, and the cotidal lines will take the form of 
curves as represented in the diagram. 



203- On what will the velocity of the tide-wave depend] 
What circumstances will retard it ? Explain figure 39. 



164 THE MOON. 

204. On account of the retarding influence of shoals, 
and an uneven, indented coast, the tide-wave travels 
more slowly along the shores of an island than in the 
neighbouring sea, assuming convex figures at a little dis- 
tance from the island and on opposite sides of it. These 
convex lines sometimes meet and become blended in 
such a manner as to create singular anomalies in a sea 
much broken by islands, as well as on coasts indented 
with numerous bays and rivers. Peculiar phenomena 
are also produced, when the tide flows in at opposite 
extremities of a reef or island, as into the two opposite 
ends of Long Island Sound. In certain cases a tide- 
wave is forced into a narrow arm of the sea, and pro- 
duces very remarkable tides. The tides of the Bay of 
Fundy (the highest in the world) sometimes rise to 
the height of 60 or 70 feet ; and the tides of the rivei 
Severn, near Bristol in England, rise to the height of 40 
feet. 

205. The Unit of Altitude of any place, is the height 
of the maximum tide after the syzigies, being usually 
about 36 hours after the new or full moon. But as the 
amount of this tide would be affected by the distance of 
the sun and moon from the earth, and by their declina- 
tions, these distances are taken at their mean value, and 
the luminaries are supposed to be in the equator ; the 
observations being so reduced as to conform to these cir- 
cumstances. The unit of altitude can be ascertained 
by observation only. The actual rise of the tide de- 
pends much on the strength and direction of the wind. 
When high winds conspire with a high flood tide, as is 
frequently the case near the equinoxes, the tide often 



204. How does the tide-wave travel along the shores of an 
island ? How are the great tides of the Bay of Fundy accounted 
for? How high do they rise there, and at Bristol in England ? 

205. Define the unit of altitude. By what circumstances is 
the unit of altitude affected ? How is it ascertained ? State 
it for several places. 



TIDES. 165 

rises to a very unusual height. We subjoin from the 
American Almanac a few examples of the unit of alti- 
tude for different places. 

Feet. 

Cumberland, head of the Bay of Fundy, 71 
Boston, 11| 

New Haven, 8 

New York, 5 

Charleston, S. C, 6 

206. The Establishment of any port is the mean in- 
terval between noon and the time of high water, on the 
day of new or full moon. As the interval for any given 
place is always nearly the same, it becomes a criterion 
of the retardation of the tides at that place. On ac- 
count of the importance to navigation of a correct 
knowledge of the tides, the British Board of Admiralty, 
at the suggestion of the Royal Society, recently issued 
orders to their agents in various important naval stations, 
to have accurate observations made on the tides, with 
the view of ascertaining the establishment and various 
other particulars respecting each station ; and the gov- 
ernment of the United States is prosecuting similar in- 
vestigations respecting our own ports. 

207. According to Professor Whewell, the tides on 
the coast of North America are derived from the great 
tide-wave of the South Atlantic, which runs steadily 
northward along the coast to the mouth of the Bay of 
Fundy, where it meets the northern tide-wave flowing 
in the opposite direction. Hence he accounts for the 
high tides of the Bay of Fundy. 

208. The largest lakes and inland seas have no per- 
ceptible tides. This is asserted by all writers respect- 



206. What is the establishment of a port ? What efforts 
have been made to obtain accurate observations on the tides ? 



166 THE MOON. 

ing the Caspian and Euxine, and the same is found to 
be true of the largest of the North American lakes, 
Lake Superior. 

Although these several tracts of water appear large 
when taken by themselves, yet they occupy but small 
portions of the surface of the globe, as will appear ev- 
ident from the delineation of them on an artificial globe. 
Now we must recollect that the primitive tides are pro- 
duced by the unequal action of the sun and moon upon 
the different parts of the .earth ; and that it is only at 
points whose distance from each other bears a consider- 
able ratio to the whole distance of the sun or the moon, 
that the inequality of action becomes manifest. The 
space required is larger than either of these tracts of 
water. It is obvious also that they have no opportunity 
to be subject to a derivative tide. 

209. To apply the theory of universal gravitation to 
all the varying circumstances that influence the tides, 
becomes a matter of such intricacy, that La Place pro- 
nounces " the problem of the tides" the most difficult 
problem of celestial mechanics. 

210. The Atmosphere that envelops the earth, must 
evidently be subject to the action of the same forces as 
the covering of waters, and hence we might expect a 
rise and fall of the barometer, indicating an atmospheric 
tide corresponding to the tide of the ocean. La Place 
has calculated the amount of this aerial tide. It is too 
inconsiderable to be detected by changes in the barom- 
eter, unless by the most refined observations. Hence it 
is concluded, that the fluctuations produced by this cause 
are too slight to affect meteorological phenomena in any 
appreciable degree. 



207. How are the tides on the coast of North America de- 
rived ? 

208. Why have lakes and seas no tides 1 

209. What is said of the difficulty of applying the principle 
of universal gravitation to all the circumstances of the tides ? 



167 



CHAPTER VII. 

OF THE PLANETS THE INFERIOR PLANETS, MERCURY 

AND VENUS. 

211. The name planet signifies a loanderer* and is 
applied to this class of bodies because they shift their 
positions in the heavens, whereas the fixed stars con- 
stantly maintain the same places with respect to each 
other. The planets known from a high antiquity, are 
Mercury, Yenus, Earth, Mars, Jupiter, and Saturn. To 
these, in 1781, was added Uranus, f (or Herschel, as it 
is sometimes called, from the name of its discoverer,) 
and, as late as 1816, another large planet, Neptune, 
was added to the list, making eight in all of the regular 
series. Besides these, there are found between Mars 
and Jupiter, a remarkable group of small planets, called 
Asteroids, numbering over thirty. Of these, four — 
Ceres, Pallas, Juno, and Yesta — were discovered near 
the commencement of the present century; and the 
remainder have been brought to light since 1845, and 
new ones are still very frequently announced. 

The planets, with the exception of the new-discovered 
Asteroids, are designated by the following characters : 

1. Mercury £ 7. Ceres ? 

2. Venus 9 8. Pallas $ 

3. Earth 9. Jupiter U 

4. Mars & 10. Saturn ^ 

5. Vesta fi 11. Uranus Jff 

6. Juno § 12. Neptune f 

The foregoing are called the primary planets. Sev- 
eral of these have one or more attendants, or satellites, 
which revolve around them, as they revolve around 

210. Has the atmosphere any tide? Is it sufficient to influ- 
ence meteorological phenomena ? 

211. Whence is the name planet derived? Which of the 

* From the Greek TrXav^r??; -j- From Ovpavos. 



168 THE PLANETS. 

the sun. The earth has one satellite, namely, the moon ; 
Jnpiter has four; Saturn, eight; Uranus, six; and 
Neptune, one. These bodies also are planets, but in 
distinction from the others they are called secondary 
planets. Hence the whole number of planetary bodies 
in the solar system is 61 — namely, 8 large primaries, 
20 secondaries, and 33 Asteroids. 

212. With the exception of the Asteroids, the primary 
planets have their orbits nearly in the same plane, and 
are never seen far from the ecliptic. Mercury, whose 
orbit is most inclined of all, never departs further from 
the ecliptic than about 7°, while most of the other 
planets pursue very nearly the same path with the earth, 
in their annual revolutions around the sun. The new 
planets, however, make wider excursions from the plane 
of the ecliptic, amounting, in the case of Pallas, to 34J°. 

213. Mercury and Yenus are called inferior planets, 
because they have their orbits nearer to the sun than 
that of the earth ; while all the others, being more dis- 
tant from the sun than the earth, are called superior 
planets. The planets present great diversity among 
themselves in respect to distance from the sun, magni- 
tude, time of revolution, and density. They differ also 
in regard to satellites, of which, as we have seen, three 
have respectively four, six, and eight, while more than 
half have none at all. It will aid the memory, and ren- 
der our view of the planetary system more clear and com- 

planets have been long known ? Which have been added in 
modern times? Mark on paper or on the black-board, the 
several characters by which the planets are designated. Dis- 
tinguish between the primary and the secondary planets. What 
is said of the Asteroids ? What bodies have satellites ? State 
the whole number of planets. 

212. Near what great circle are the orbits of all the planets? 
How far does Pallas deviate from the ecliptic ? 

213. Why are Mercury and Venus called inferior planets? 
Why are the other planets called superior? What diversities 
do the planets exhibit among themselves ? 



DISTANCES FROM THE SUN. 169 

prehensive, if we classify, as far as possible, the various 
particulars comprehended under the foregoing heads. 

214. DISTANCES FROM THE SUX. 

1. Mercury, - - - 37,000,000 

2. Venus, - - - 68,000,000 

3. Earth, - - - 95,000,000 

4. Mars, - - - 145,000,000 

5. Asteroids, - - - 250,000,000 

6. Jupiter, - - - 495,000,000 
1 Saturn, - - - 900,000,000 

8. Uranus, - - - 1800,000,000 

9. Neptune, - - - 2800,000,000 

The dimensions of the planetary system are seen from 
this table to be vast, comprehending a circular space 
towards six thousand millions of miles in diameter. A 
railway car, travelling at the rate of 20 miles an hour, 
and of course making 480 miles a day, would require 
about 50 days to travel round the earth on a great-circle, 
and about 500 days to reach the moon ; but it will give 
some idea of the vastnesss of the planetary spaces to 
reflect that, setting out from the sun and travelling from 
planet to planet at the same rate, to reach Mercury 
would require about 200 years ; Yenus, nearly 400 ; the 
Earth, 542; Mars, more than 800; Jupiter, towards 
3000 ; Saturn, above 5000 ; Uranus, 10,000 ; Neptune, 
more than 16,000 ; and to cross the entire orbit of 
Neptune (the present boundary of the planetary system), 
would require upwards of 32,000 years. 

Diagrams and orreries, as usually constructed, wholly 
fail of giving any just conceptions of the distances of 
the planets from the Sun and from each other. If we 

214. State the distance of each of the planets from the sun. 
What is said of the dimensions of the planetary system ? How 
do the distances of those planets which are nearest the sun in- 
crease ? Also those which are more distant ? How may the 
mean distances of the planets from the sun he determined? 
Give an example in computing the distance of Jupiter. What 
is said of diagrams and orreries ? 

15 



170 THE PLANETS. 

represent, for instance, the distance of the Earth by 
1 loot, we shall require 30 feet in order to reach the 
place of Neptune; and when we have constructed a 
diagram on so large a scale, we must still recollect that 
each foot represents a space of nearly 100 millions 
of miles. 

It may aid the memory to remark, that in regard to 
the planets nearest the sun, the distances increase in an 
arithmetical ratio, while those most remote, increase in 
a geometrical ratio. Thus, if we add 30 to the distance 
of Mercury, it gives us nearly that of Yenus ; 30 more 
gives that of the Earth ; while Saturn is nearly twice 
the distance of Jupiter, and Uranus twice the distance 
of Saturn. Between the orbits of Mars and Jupiter, a 
great chasm appeared, which broke the continuity of 
the series ; but the discovery of the new planets has 
filled the void. 

The mean distances of the planets from the sun, may 
be determined by means of Kepler's law, that the squares 
of the periodical times are as the cubes of the distances. 
Thus the earth's distance being previously ascertained 
bj means of the sun's horizontal parallax, and the pe- 
riod of any other planet, as Jupiter, being learned from 
observation, we say as 365.256 2 : 4332.585 2 * : : l 3 : 
5.202 3 , which equals the cube of Jupiter's distance from 
the sun, and its root equals that distance itself. 



215. MAGNITUDES. 



Mercury, 

Venus, 

Earth, 

Mars, 

Ceres, 

Jupiter, 

Saturn, 

Uranus, 

Neptune, 



Diam. in Miles. 


Volume. 


2950 


1 
T9 


7800 


9 
To" 


7912 


1 


4500 


1 


160 




89000 


1400 


79000 


1000 


35000 


86 


31000 


60 



* This is the number of days in one revolution of Jupiter. 



PERIODIC TIMES. 



171 



"We remark here a great diversity in regard to magni- 
tude, a diversity which does not appear to be subject to 
any definite law. While Venus, an inferior planet, is 
T \ as large as the earth, Mars, a superior planet, is only 
J, while Jupiter is 1400 times as large. Although several 
of the planets, when nearest to us, appear brilliant and 
large when compared with the fixed stars, yet the angle 
which they subtend is very small, that of Venus, the 
greatest of all, never exceeding about 1', or more exact- 
ly 61".9, and that of Jupiter being when greatest only 



about | of a minute. 








216. 


PERIODIC 


TIMES. 




Kevolution in its orbit 




Mean daily motion 


Mercury, 3 months 


or 88 


days, 


4° 5' 32".6 


Venus, 7J " 


224 


" 


1° 36' 7".8 


Earth, 1 year, 


365 


" 


0° 59' 8".3 


Mars, 2 years, 


" 687 


" 


0° 31' 26".7 


Ceres, 4-J " 


" 1687 


a 


0° 12' 50".9 


Jupiter, 12 " 


" 4332 


a 


0° 4' 59".3 


Saturn, 29 " 


" 10759 


a 


0° 2' 0".6 


Uranus, 84 " 


" 30686 


U 


0° 0' 42".4 


Neptune, 164±- " 


" 60127 


" 


0° 0' 21".5 



From this view, it appears that the planets nearest 
the sun move most rapidly. Thus Mercury performs 
nearly 350 revolutions while Uranus performs one. 
This is evidently not owing merely to the greater dimen- 
sions of the orbit of Uranus, for the length of its orbit 
is not 50 times that of the orbit of Mercury, While the 



215. State the diameter of each of the planets. What diver- 
sities occur in regard to their magnitudes ? How great angles 
do Venus and Jupiter subtend ? 

216. State the periodic time of each of the planets. Which 
planets move most rapidly ? How many revolutions does Mer- 
cury perform while Uranus performs one ? What is the daily 
rate of Uranus ? 



172 THE PLANETS. 

time employed in describing it is 350 times that of 
Mercury. Indeed this ought to follow from Kepler's 
law, that the squares of the periodical times are as the 
cubes of the distances ; from which it is manifest that 
the times of revolution increase faster than the dimen- 
sions of the orbit. Accordingly, the apparent progress 
of the most distant planets is exceedingly slow, the 
daily rate of Uranus being only 42" .4 per day ; so that 
for weeks and months, and even years, this planet but 
slightly changes its place among the stars. 

THE INFERIOR PLANETS, MERCURY AND VENUS. 

217. The inferior planets, Mercury and Yenus, hav- 
ing their orbits so far within that of the earth, appear 
to us as attendants upon the sun. Mercury never ap- 
pears further from the sun than 29° (28° 48'), and seldom 
so far ; and Yenus never more than about 47° (47° 12'). 
Both planets, therefore, appear either in the west soon 
after sunset, or in the east a little before sunrise. In 
high latitudes, where the twilight is prolonged, Mercury 
can seldom be seen with the naked eye, and then only 
at the periods of its greatest elongation.* The reason 
of this will readily appear from the following diagram. 

Let S (Fig. 40) represent the sun, ADB the orbit of 
Mercury, and E the place of the Earth. Each of the 
planets is seen at its greatest elongation, when a line, 
EA or EB in the figure, is a tangent to its orbit. Then 
the sun being at S' in the heavens, the planet will be 
seen at A' and B', when at its greatest elongations, and 
will appear no further from the sun than the arc S'A' 
or S'B' respectively. 



217. What is Mercury's greatest elongation from the sun? 
"What is Vemis's ? What is said respecting the difficulty of 
seeing Mercury ? Explain by figure 40. 

* Copernicus is said to have lamented on his death-bed that he had 
never been able to obtain a sight of Mercury, and Delambre saw it 
but twice. 



MERCURY AND VENUS. 



m 



Fig. 40. 




218. A planet is said to be in conjunction with the 
sun, when it is seen in the same part of the heavens 
with the sun, or when it has the same longitude. Mer- 
cury and Yenus have each two conjunctions, the infe- 
rior and the superior. The inferior conjunction is its 
position when in conjunction on the same side of the 
sun with the earth, as at C in the figure : the superior 
conjunction is its position when on the side of the sun 
most distant from the earth, as at D. 

219. The period occupied by a planet between two 
successive conjunctions with the earth, is called its sy- 
nodical revolution. Both the planet and the earth be- 



218. "When is a planet said to be in conjunction with the 
sun ? What conjunctions have the inferior planets ? 

219. Define the synodical revolution. How does this period 
compare with the sidereal revolution ? Explain by figure 40. 
What is the synodical period of Mercury and Venus respectively ? 

15* 



1*74 THE PLANETS. 

ing in motion, the time of the synodical revolution ex- 
ceeds that of the sidereal revolution of Mercury or 
Yenus ; for when the planet comes round to the place 
where it before overtook the earth, it does not find the 
earth at that point, but far in advance of it. Thus, let 
Mercury come into inferior conjunction with the earth 
at C, (Fig. 40.) In about 88 days the planet will come 
round to the same point again ; but meanwhile the 
earth has moved forward through the arc EE', and will 
continue to move while the planet is moving more 
rapidly to overtake her, the case being analogous to 
that of the hour and minute hand of a clock. 

The synodical period of Mercury is 116, and of Ye- 
nus 584 days. 

220. TJie motion of an inferior planet is direct in 
passing through its superior conjunction, and retrograde 
in passing through its inferior conjunction. Thus Ye- 
nus, while going from B through D to A, (Fig. 40,) 
moves in the order of the signs, or from west to east, 
and would appear to traverse the celestial vault B'S'A' 
from right to left ; but in passing from A through C to 
B, her course would be retrograde, returning on the 
same arc from left to right. If the earth were at rest, 
therefore, (and the sun, of course, at rest,) the inferior 
planets would appear to oscillate backwards and for- 
wards across the sun. But, it must be recollected, that 
the earth is moving in the same direction with the 
planet, as respects the signs, but with a slower motion. 
This modifies the motions of the planet, accelerating it 
in the superior and retarding it in the inferior conjunc- 
tion. Thus in figure 40, Yenus while moving through 
BDA would seem to move in the heavens from B' to 



220. When is the motion of an inferior planet direct and 
when retrograde ? Explain by figure 40. If the earth were at 
rest, how would the inferior planets appear to move ? Show 
how the earth's motion modifies the apparent motions. 



MERCURY AND VENUS. 175 

A', were the earth at rest ; but meanwhile the earth 
changes its position from E to E', by which means the 
planet is not seen at A' but at A", being accelerated 
by the arc A'A" in consequence of the earth's motion. 
On the other hand, when the planet is passing through 
its inferior conjunction ACB, it appears to move back- 
wards in the heavens from A' to B' if the earth is at 
rest, but from A' to B" if the earth has in the mean 
time moved from E to E', being retarded by the arc 
B'B". Although the motions of the earth have the 
effect to accelerate the planet in the superior conjunc- 
tion, and to retard it in the inferior, yet, on account of 
the greater distance, the apparent motion of the planet 
is much slower in the superior than in the inferior con- 
junction. 

221. When passing from the superior to the inferior 
conjunction, or from the inferior to the superior con- 
junction, through the greatest elongations, the inferior 
planets are stationary. 

If the earth were at rest, the stationary points would 
be at the greatest elongations, as at A and B, for then the 
planet would be moving directly towards or from the 
earth, and would be seen for some time in the same 
place in the heavens ; but the earth itself is moving 
nearly at right angles to the line of the planet's motion, 
that is, the line which is drawn from the earth to the 
planet through the point of greatest elongation ; hence a 
direct motion is given to the planet by this cause. When 
the planet, however, has passed this line, by its superior 
velocity it soon overcomes this tendency of the earth 
to give it a relative motion eastward, and becomes 
retrograde as it approaches the inferior conjunction. 



221. When are the inferior planets stationary ? Why are 
they not stationary at the points of greatest elongation % At 
what elongation are Mercury and Venus stationary respect- 
ively ? 



176 THE PLANETS. 

Its stationary point obviously lies between its place of 
greatest elongation and the place where its motion be- 
comes retrograde. Mercury is stationary at an elon- 
gation of from 15° to 20° from the sun ; and Venus at 
about 29°. 

222. Mercury and Venus exhibit to the telescope pha- 
ses similar to those of the moon. 

"When on the side of their inferior conjunction, these 
planets appear horned, like the moon in her first and 
last quarters ; and when on the side of their superior 
conjunctions they appear gibbous. At the moment of 
superior conjunction, the whole enlightened orb of the 
planet is turned towards the earth, and the appearance 
would be that of the full moon, but the planet is too 
near the sun to be commonly visible. 

These different phases show that these bodies are opake, 
and shine only as they reflect to us the light of the sun ; 
and the same remark applies to all the planets. 

223. The orbit of Mercury is the most eccentric, and 
the most inclined of all the planets /* while that of Ve- 
nus varies but little from a circle, and lies much nearer 
to the ecliptic. 

The eccentricity of the orbit of Mercury is nearly \ 
^ its semi-major axis, while thatofYenus is only T J 3-; 
the inclination of Mercury's orbit is 7°, while that of 
Yenus is less than 3J°. Mercury, on account of his dif- 
ferent distances from the earth, varies much in his ap- 



222. What phases do Mercury and Venus exhibit? Explain 
by figure 40. Whence do these bodies derive their light ? Is 
the same true of the other planets ? 

223. What is said of the eccentricity and inclination of the 
orbit of Mercury ? How does the apparent diameter of Mer- 
cury vary ? How are his changes of seasons ? 

* The new planets of course excepted. 



MERCURY AND VENUS. 177 



parent diameter, which is only 5" in the apogee, but 
12" in the perigee. The inclination of his orbit to his 
equator being very great, the changes of his seasons 
must be proportionally great. 

These different aspects of an inferior planet will be 
easily understood from Fig. 41, where the earth is at E, 




and the planet is represented in various positions in its 
revolutions around the sun. When at A, in the supe- 
rior conjunction, the whole enlightened disk is turned 
towards us ; at D, in the inferior conjunction, the en- 
lightened side is turned entirely from us ; and at the 
quadratures B and C half the disk is in view. Between 
A and B and A and C the planet is gibbous, like the 
moon in her second and third quarters ; and between B 
and D and C and D the planet is horned, like the moon 
in her first and last quarters. 

224. An inferior planet is brightest at a certain 
point between its greatest elongation and inferior con- 
junction. 

Its maximum brilliancy would happen at the inferior 
conjunction, (being then nearest to us,) if it shinecl by 



224. "When is an inferior planet brightest? Why not when, 
nearest to us ? Why not when most of the illuminated side is 
turned towards us ? 



1?8 



THE PLANETS. 



its own light; but in that position its dark side is 
turned towards us. Still, its maximum cannot be when 
most of the illuminated side is towards us ; for then, 
being at the superior conjunction, it is at its greatest 
distance from us. The maximum must therefore be 
somewhere between the two. Yenus gives her greatest 
light when about 40° from the sun. 

225. Mercury and Yenus loth revolve on their axes^ 
in nearly the same time with the earth. 

The diurnal period of Mercury is 24h. 5m.' 28s., and 
that of Yenus 23h. 21m. 7s. The revolutions on their 
axes have been determined by means of some spot or 
mark seen by the telescope, as the revolution of the sun 
on his axis is ascertained by means of his spots. 

226. Yenus is regarded as the most beautiful of the 
planets, and is well known as the morning and evening 
star. The most ancient nations did not, indeed, recog- 
nize the evening and morning star as one and the same 
body, but supposed they were different planets, and 
accordingly gave them different names, calling the 
morning star Lucifer, and the evening star Hesperus. 
At her period of greatest splendor, Yenns casts a 
shadow, and is sometimes visible in broad daylight. 
Her light is then estimated as equal to that of twenty 
stars of the first magnitude. At her period of greatest 
elongation, Yenus is visible from three to four hours 
after the setting or before the rising of the sun. 

227. Every eight years Yenus forms her conjunctions 
with the sun in the same part of the heavens. 



225. In what time do Mercury and Venus, respectively, re- 
volve on their axes ? How are these periods ascertained ? 

226. What erroneous notions had the ancients respecting the. 
morning and evening star ? What is said of the brilliancy of 
Venus at her greatest splendor ? How long may Venus be in 



sight after sunset ? 



MERCURY AND VENUS. 1*79 

For, since the synodical period of Venus is 584 days, 
and her sidereal period 224.7, 

224.7 : 360° : : 584 : 935.6 = the arc of longitude de- 
scribed by Verms between the first and second conjunc- 
tions. Deducting 720°, or two entire circumferences, 
the remainder, 2 15°. 6, shows how far the place of the 
second conjunction is in advance of the first. Hence, 
in five synodical revolutions, or 2920 days, the same 
point must have advanced 215°.6 x5= 1078°, which is 
nearly three entire circumferences, so that at the end of 
five synodical revolutions, occupying 2920 days, or 8 
years, the conjunction of Venus takes place nearly in 
the same place in the heavens as at first. 

Whatever appearances of this planet, therefore, arise 
from its position with respect to the earth and the sun, 
they are repeated every eight years in nearly the same 
form. 

TRANSITS OF THE INFERIOR PLANETS. 

228. The Transit of Mercury or Venus, is its pas- 
sage across the surfs disk, as the moon passes over it in 
a solar eclipse. 

As a transit takes place only when the planet is in 
inferior conjunction, at which time her motion is retro- 
grade, it is always from left to right, and the planet is 
seen projected on the solar disk in a black round spot. 
Were the orbits of the inferior planets coincident with 
the plane of the earth's orbit, a transit would occur to 
some part of the earth at every inferior conjunction. 
But the orbit of Venus' makes an angle of 3 J° with the 
ecliptic, and Mercury an angle of 7° ; and, moreover, 
the apparent diameter of each of these bodies is very 



227. What happens to Venus every eight years? 

228. What is meant by the transit of Mercury or Venus ? 
When only can a transit take place ? What angles do the or- 
bits of Venus and Mercury respectively make with the ecliptic ? 
In what months does the sun pass through the nodes of each of 
these planets ? 



180 THE PLANETS. 

small, both of which circumstances conspire to render a 
transit a comparatively rare occurrence, since it can 
happen only when the sun, at the time of an inferior 
conjunction, chances to be at or extremely near the 
planet's node. The nodes of Mercury lie in that part 
of the earth's orbit which the sun passes through in 
May and November. It is only in these months, there- 
fore, that transits of Mercury can occur. For a similar 
reason, those of Venus occur only in June and Decem- 
ber. Since, however, the nodes of both planets have a 
small retrograde motion, the months in which transits 
occur will change in the course of ages. 

229. Transits of Mercury occur more frequently than 
those of Yenus. The periodic times of Mercury and 
the earth are so adjusted to each other, that Mercury 
performs nearly 29 revolutions while the earth per- 
forms 7. If, therefore, the two bodies meet at the node 
in any given year, seven years afterwards they will 
meet nearly at the same node, and a transit may take 
place, accordingly, at intervals of 7 years. But 54: 
revolutions of Mercury correspond still nearer to 13 
revolutions of the earth, and therefore a transit is still 
more probable after intervals of 13 years. At intervals 
of 33 years, transits of Mercury are exceedingly proba- 
ble, because in that time Mercury makes almost exactly 
137 revolutions. Intermediate transits however may 
occur at the other node, these intervals having reference 
merely to the same node. Thus transits of Mercury 
happened at the ascending node in 1815, and 1822, at 
intervals of 7 years ; and at the descending node in 
1832, which returned in 1815, after an interval of 13 



229. Which planet lias the most frequent transits? What 
is the shortest interval of the transits of Mercury ? What are 
the longer intervals ? When will the next occur ? What are 
intervals of the transits of Venus ? When was the last transit of 
Venus, and when will the next occur ? 



3LERCURY AND VENUS. 181 

years. Transits of Venus are much more unfrequent 
than those of Mercury. Eight revolutions of the earth 
are completed in nearly the same time as thirteen revo- 
lutions of Venus, and hence two transits of Venus may 
occur at an interval of 8 years, as was the case at the 
last return of this phenomenon, one transit having oc- 
curred in 1761, and another in 1769. But if a transit 
does not happen after 8 years, it will not happen, at the 
same node, until an interval of 235 years ; but inter- 
mediate transits may occur at the other node. The 
next transit of Venus will take place in 1874, being 235 
years after the first that was ever observed, which oc- 
curred in the year 1639. In the mean time, as already 
mentioned, two transits have occurred at the other node, 
at intervals of 8 years. 

230. The great interest attached by astronomers to a 
transit of Venus, arises from its furnishing the most ac- 
curate means in our power of determining the surfs 
horizontal parallax — an element of great importance, 
since it leads us to a knowledge of the distance of the 
earth from the sun, and, consequently, by the applica- 
tion of Kepler's law, (Art. 130,) of the distances of all 
the other planets. Hence, in 1769, great efforts were 
made throughout the civilized world, under the patron- 
age of different governments, to observe this phenome- 
non under circumstances the most favorable for deter- 
mining the parallax of the sun. 

The common methods of finding the parallax of a 
heavenly body cannot be relied on to a greater degree 
of accuracy than 4". In the case of the moon, whose 
greatest parallax amounts to about 1°, this deviation 
from absolute accuracy is not material ; but it amounts 
to nearly half the entire parallax of the sun. 



230. Why is so much interest attached to the transits of 
Venus ? What efforts were made to observe it in 1769 ? Why 
cannot we ascertain the horizontal parallax of the sun in the 
same way as we do that of the moon ? 

16 



182 THE PLANETS. 

231. If the sun and Yenus were equally distant from 
us, they would be equally affected by parallax as view- 
ed by spectators in different parts of the earth, and 
hence their relative situation would not be altered by 
it; but since Yenus, at the inferior conjunction is only 
about one third as far off as the sun, her parallax is pro- 
portionally greater, and therefore spectators at distant 
points will see Yenus projected on different parts of the 
solar disk, as the planet traverses the disk. Astron- 
omers avail themselves of this circumstance to ascer- 
tain the sun's horizontal parallax. In order to make 
the difference as large as possible, very distant places 
are selected for observation. Thus in the transit of 
1769, among the places selected, two of the most favor- 
able were "Wardhuz in Lapland, and Tahiti, one of 
the South Sea Islands. 

The appearance of Yenus on the sun's disk being 
that of a well-defined black spot, and the exactness with 
which the moment of external or internal contact may 
be determined, are circumstances favorable to the ex- 
actness of the result ; and astronomers repose so much 
confidence in the estimation of the sun's horizontal 
parallax as derived from the observations on the transit 
of 1769, that this important element is thought to be 
ascertained within -^ of a second. The general result 
of all these observations gives the sun's horizontal 
parallax 8".6, or more exactly, 8".5776. 

232. The elder astronomers imagined they had dis- 
covered a satellite accompanying Yenus in her transit. 
If Yenus had in reality any satellite, the fact would be 
obvious at her transits, as the satellite would be pro- 
jected near the primary on the sun's disk; but later 



231. How is Yenus projected on the sun to spectators in 
different parts of the earth ? What places were selected for 
observing the transit of 1769 ? 

232, Has Venus any Satellite? 



SUPERIOR PLANETS. 183 

astronomers have searched in vain for any appearances 
of the kind, and the inference is, that former astronomers 
were deceived by some optical illusion. 



CHAPTER VIII. 

OF THE SUPERIOR PLANETS MARS, JUPITER, SATURN, 

URANUS, AND NEPTUNE 'ASTEROIDS. 

233. The Superior planets are distinguished from the 
Inferior, by being seen at all distances from the sun 
from 0° to 180°. Having their orbits exterior to that 
of the earth, they of course never come between us and 
the sun, that is, they never have any inferior conjunction 
like Mercury and Yenus, but they are sometimes seen in 
superior conjunction, and sometimes in opposition. Nor 
do they, like the inferior planets, exhibit to the telescope 
different phases, but, with a single exception, they al- 
ways present the side that is turned towards the earth 
fully enlightened. This is owing to their great distance 
from the earth ; for were the spectator to stand upon the 
sun, he would of course always have the illuminated 
side of each of the planets turned towards him ; but, so 
distant are all the superior planets except Mars, that 
they are viewed by us very nearly in the same manner 
as they would be if we actually stood on the sun. 

234. Mars is a small planet, his diameter being only 
about half of that of the earth, or 4500 miles. He also, 
at times, comes nearer to the earth than any other planet 



233. Name the Superior Planets. How are they distin- 
guished from the Inferior? Which of them exhibit phases? 
Why do not the rest ? 

234. Mars. — State his diameter — mean distance from the 
sun — inclination of his orbit. How distinguished from the 
other planets ? Why do his brightness and apparent magnitude 
vary so much ? Illustrate by figure 42. 



184 



THE PLANETS. 



except Venus. His mean distance from the sun is 
14:5,000,000 miles; but his orbit is so eccentric that his 
distance varies much in different parts of his revolution, 
Mars is always very near the ecliptic, never varying from 
it 2°. Pie is distinguished from all the planets by his 
deep red color, and hery aspect ; but his brightness and 
apparent magnitude vary much at different times, being 
sometimes nearer to us than at others, by the whole di- 
ameter of the earth's orbit, that is, by about 190,000,000 
of miles. When Mars is on the same side of the sun 
with the earth, or at his opposition, he comes within 
47,000,000 miles of the earth, and rising about the time 
the sun sets, surprises us by his magnitude and splendor ; 
but when he passes to the other side of the sun to his 
superior conjunction, he dwindles to the appearance of 
a small star, being then 237,000,000 miles from us. Thus, 
let M (Fig. 42) represent Mars in opposition, and M' 
in the superior conjunction, while E represents the earth. 
It is obvious that in the former situation, the planet 
must be nearer to the earth than in the latter by the 
whole diameter of the earth's orbit. 

Fig. 42. 




MARS. 185 

235. Mars is the only one of the superior planets 
which exhibits phases. When he is towards the quad- 
ratures at Q or Q', it is evident from the figure that 
only a part of the circle of illumination is turned towards 
the earth, such a portion of the remoter part of it being 
concealed from our view as to render the form more or 
less gibbous. 

236. When viewed with a powerful telescope, the 
surface of Mars appears diversified with numerous vari- 
eties of light and shade. The region around the poles 
is marked by white spots, which vary their appearance 
with the changes of seasons in the planets. Hence Dr. 
Herschel conjectured that they were owing to ice and 
snow, which alternately accumulates and melts, according 
to the position of each pole with respect to the sun. It 
has been common to ascribe the ruddy light of this plan- 
et to an extensive and dense atmosphere, which was said 
to be distinctly indicated by the gradual diminution of 
light observed in a star as it approached very near to the 
planet in undergoing an occultation; but more recent 
observations afford no such evidence of an atmosphere. 

237. By observations on the spots, we learn that Mars 
revolves on his axis in very nearly the same time with 
the earth, (24h. 39m. 21s.3 ;) and that the inclination 
of his axis to that of his orbit is also nearly the same, 
being 28° 42'. 

As the diurnal rotation of Mars is nearly the same as 
that of the earth, we might expect a similar flattening at 
the poles, giving to the planet a spheroidal figure. In- 



235. Show why Mars should exhibit phases. 

236. How is the surface of Mars diversified? What is seen 
around the poles ? What indications are there of ice and snow ? 
To what is the ruddy hue of Mars ascribed ? 

237. How do we learn his revolution on his axis? In what 
time does it take place ? What is the figure of Mars ? How 
does its ellipticity compare with that of the earth ? 

16* 



186 THE PLACETS. 

deed the compression or ellipticity of Mars is six times 
that of the earth. This remarkable flattening of the 
23oles of Mars has been supposed to arise from a great 
variation of density in the planet in different parts. 

238. Jupiter is distinguished from all the other plan- 
ets by his vast magnitude. His diameter is more than 
11 times, and his volume is 1400 times that of the earth. 
His figure is strikingly spheroidal, the equatorial being 
larger than the polar diameter in the proportion of 107 
to 100. Such a figure might naturally be expected 
from the rapidity of his diurnal rotation, which is ac- 
complished in about 10 hours. A place on the equator 
of Jupiter must turn 27 times as fast as on the terrestrial 
equator. The distance of Jupiter from the sun is 
495,000,000 miles, and his revolution around the sun 
occupies nearly 12 years. 

239. The view of Jupiter through a good telescope, 
(Fig. 43,) is one of the most magnificent and interesting 

Fig. 43. 




spectacles in astronomy. The disk expands into a large 
and bright orb like the full moon ; the spheroidal figure 



238. Jupiter. — State his diameter, volume, figure, revolution 
on his axis, velocity of his equator, distance from the sun, periodic 
time. 



JUPITER. 187 

which theory assigns to revolving spheres, is here pal- 
pably exhibited to the eye ; across the disk 5 arranged 
in parallel stripes, are discerned several dusky bands, 
called belts; and four bright satellites, always in at- 
tendance, and ever varying their positions, compose a 
splendid retinue. Indeed, astronomers gaze with |>eeuliar 
interest on Jupiter and his moons, as affording a minia- 
ture representation of the whole solar system, repeating 
on a smaller scale, the same revolutions, and exemplify- 
ing, in a manner more within the compass of our ob- 
servation, the same laws as regulate the entire assem- 
blage of sun and planets. 

240. The Belts of Jupiter, are variable in their num- 
ber and dimensions. With the smaller telescopes, only 
one or two are seen across the equatorial regions; but 
with more powerful instruments, the number is in- 
creased, covering a great part of the whole disk. Dif- 
ferent opinions have been entertained by astronomers 
respecting the cause of the belts ; but they have gen- 
erally been regarded as clouds formed in the atmosphere 
of the planet, agitated by winds, as is indicated by their 
frequent changes, and made to assume the form of belts 
parallel to the equator by currents that circulate around 
the planet like the trade winds and other currents that 
circulate around our globe. Sir John Herschel supposes 
that the belts are not ranges of clouds, but portions of 
the planet itself brought into view by the removal of 
clouds and mists, that exist in the atmosphere of the 
planet through which are openings made by currents 
circulating around Jupiter. 

241. The Satellites of Jupiter may be seen with a 
telescope of very moderate powers. Even a common 
spy-glass will enable us to discern them. Indeed, one 



239. What does the telescopic view of Jupiter exhibit ? Why 
do astronomers regard it with so much interest ? 

240. Describe Jupiter's Belts — to what are they ascribed ? 



188 



THE PLANETS. 



or two of them have been occasionally seen with the 
naked eye. In the largest telescopes, they severally 
appear as bright as Sirins. With such an instrument, 
the view of Jupiter with his moons and belts is truly a 
magnificent spectacle, a world within itself. As the 
orbits of the satellites do not deviate far from the plane 
of the ecliptic, and but little from the equator of the 
planet, they are usually seen in nearly a straight line with 
each other, extending across the central part of the disk. 

242. Jupiter's satellites are distinguished from one 
another by the denominations of first, second, third, and 
fourth* according to their relative distances from Jupi- 
ter, the first being that which is nearest to him. Their 
apparent motion is oscillatory, like that of a pendulum, 
going alternately from their greatest elongation on one 
side to their greatest elongation on the other, sometimes 
in a straight line, and sometimes in an elliptical curve, 
according to the different points of view in which we 
observe them from the earth. They are sometimes sta- 
tionary ; their motion is alternately direct and retro- 
grade ; and, in short, they exhibit in miniature all the 
phenomena of the planetary system. Various partic- 
ulars of the system are exhibited in the following table. 
The diameters and distances are given in miles. 



Satellites. 


Diameter. 


Distances. 


Sidereal Kevolution. 


1 
2 
3 
4 


2440 
2190 
3580 
3060 


278,500 

443,300 

707,000 

1,243,000 


Id. 18h. 28m. 
3 13 15 
7 3 43 
16 16 32 



Hence, it appears, first, that Jupiter's satellites are all, 



241. How do the satellites appear to the telescope? 

242. Describe the motions of the satellites — magnitudes — 
distances — periods of revolution. 



* The classical names of Jupiter's satellites, are Io, Europa, Gany- 
mede, Calisto. 



JUPITER. 189 

except the second, somewhat larger than the moon, but 
that the second satellite is the smallest, and the third the 
largest of the whole, although the diameter of the latter 
is only about -j-j part of that of the primary ; secondly, 
that the distance of the innermost satellite from the 
planet is 40,000 miles further than that of the moon 
from the earth, while that of the outermost satellite 
stretches off to the distance of a million and a quarter 
miles; thirdly, that the first satellite completes his 
revolution around the primary in one day and three 
fourths, while the fourth satellite requires nearly sixteen 
and three fourths days. 

243. The orbits of the satellites are nearly or quite 
circular, and deviate but little from the plane of the 
planet's equator, and of course are but slightly inclined 
to the plane of its orbit. They are, therefore, in a sim- 
ilar situation with respect to Jupiter as the moon would 
be with respect to the earth if her orbit nearly coincided 
with the ecliptic, in which case she would undergo an 
eclipse at -every opposition. 

244. The eclipses of Jupiter's satellites, in their gen- 
eral conception, are perfectly analogous to those of the 
moon, but in their detail they differ in several particulars. 
Owing to the much greater distance of Jupiter from the 
sun, and its greater magnitude, the cone of its shadow is 
much longer and larger than that of the earth. On this 
account, as well as on account of the little inclination of 
their orbits to that of their primary, the three inner sat- 
ellites of Jupiter pass through the shadow, and are totally 
eclipsed at every revolution. The fourth satellite, owing 
to the greater inclination of its orbit, sometimes though 



243. What is the shape of their orbits ? How situated with 
regard to the plane of the planet's orbit ? 

244. Describe the phenomena of their eclipses. Which of 
them escapes an eclipse ? Are these eclipses seen in different 
parts of the earth at the same moment of absolute time? 



190 THE PLANETS. 

rarely escapes eclipse, and sometimes merely grazes the 
limits of the shadow or suffers a partial eclipse. These 
eclipses, moreover, are not seen, as is the case with 
those of the moon, from the center of their motion, but 
from a remote station, and one whose situation with 
respect to the line of the shadow is variable. This, of 
course, makes no difference in the times of the eclipses, 
but a very great one in their visibility, and in their 
apparent situations with respect to the planet at the 
moment of their entering or quitting the shadow. 

245. The eclipses of Jupiter's satellites present some 
curious phenomena, which will be understood from the 
following diagrams. 

Fig. 44. 





Let A, B, C, D, (Fig. 44,) represent the earth in dif- 
ferent parts of its orbit ; J, Jupiter in his orbit sur- 
rounded by his four satellites, the orbits of which are 
marked 1, 2, 3, 4. At a the first satellite enters the 
shadow of the planet, and emerges from it at 5, and ad- 
vances to its greatest elongation at c. The other satellites 



245. Describe the phenomena of the eclipses from figure 44. 
Will these appearances be affected by the relative position of 
the earth, with respect to the planet? Does the shadow of a 
satellite or the satellite itself ever make a transit across the disk 
of the planet ? 



JUPITER. 191 

traverse the shadow in a similar manner. These ap- 
23earances will be modified by the place the earth hap- 
pens to occupy in its orbit, being greatly altered by per- 
spective ; but their appearances for any given night as 
exhibited at Greenwich, are calculated and accurately 
laid down in the Nautical Almanac. 

When one of the satellites is passing between Jupi- 
ter and the sun, it casts its shadow on the primary as the 
moon casts its shadow on the earth in a solar eclipse. 
We see with the telescope, the shadow traversing the 
disk. Sometimes the satellite itself is seen projected on 
the disk ; but being illuminated as well as the primary, 
it is not so easily distinguished as Yenus or Mercury 
when seen on the sun's disk, since, at the time of their 
transits, their dark sides are turned towards us. The 
manner in which these phenomena take place, as seen 
from the earth in the several positions, A, B, C, D, may 
be conceived by attentively inspecting the figure. It 
will be seen, that when the earth is at A or C, the im- 
mersions and emersions must take place close to the disk 
of the planet, but that, in other positions of the earth, 
as at B or D, the satellite will be seen to enter and leave 
the shadow at some distance from the primary. 

246. The eclipses of Jupiter's satellites have been 
studied with great attention by astronomers, on account 
of their affording one of the easiest methods of deter- 
mining the longitude. On this subject Sir J. Herschel 
remarks : The discovery of Jupiter's satellites by Galileo, 
which was one of the first fruits of the invention of the 
telescope, forms one of the most memorable epochs in 
the history of astronomy. The first astronomical solution 
of the great problem of "the longitude," — the most 
important problem for the interests of mankind, that has 



246. Why have the eclipses of Jupiter's satellites been studied 
with so much attention ? Who first discovered these eclipses ? 
What bearing has the system of Jupiter and his satellites upon 
the Copernican system of astronomy ? 



192 THE PLANETS. 

ever been brought under the dominion of strict scientific 
principles, dates immediately from their discovery. The 
final and conclusive establishment of the Copernican 
system of astronomy, may also be considered as refer- 
able to the discovery and study of this exquisite minia- 
ture system, in which the laws of the planetary motions, 
as ascertained by Kepler, and especially that which 
connects their periods and distances, were speedily 
traced, and found to be satisfactorily maintained. 

247. The entrance of one of Jupiter's satellites into 
the shadow of the primary being seen like the entrance 
of the moon into the earth's shadow, at the same mo- 
ment of absolute time, at all places where the planet is 
visible, and being wholly independent of parallax ; be- 
ing, moreover, predicted beforehand with great accuracy 
for the instant of its occurrence at Greenwich, and given 
in the Nautical Almanac ; this would seem to be one of 
those events (Art. 188) which are peculiarly adapted 
for finding the longitude. It must be remarked, how- 
ever, that the extinction of light in the satellite at its 
immersion, and the recovery of its light at its emersion, 
are not instantaneous but gradual ; for the satellite, like 
the moon, occupies some time in entering into the 
shadow or in emerging from it, which occasions a pro- 
gressive diminution or increase of light. The better the 
light afforded by the telescope with which the observa- 
tion is made, the later the satellite will be seen at its 
immersion, and the sooner at its emersion.* In noting 
the eclipses even of the first satellite, the time must be 
considered as uncertain to the amount of 20 or 30 sec- 



247. Explain how these eclipses are used in finding the lon- 
gitude. What imperfections attend this method ? Is this method 
much employed at present ? Why can it not be used at sea ? 



* This is the reason why observers are directed in the Nautical Al- 
manac to use telescopes of a certain power. 



SATURN. 193 

onds; and those of the other satellites involve still 
greater uncertainty. Two observers, in the same room, 
observing with different telescopes the same eclipse, 
will frequently disagree in noting its time to the amount 
of 15 or 20 seconds ; and the difference will be always 
the same way. 

Better methods, therefore, of finding the longitude are 
now employed, although the facility with which the 
necessary observations can be made, and the little calcu- 
lation required, still render this method eligible in many 
cases where extreme accuracy is not important. As a 
telescope is essential for observing an eclipse of one of 
the satellites, it is obvious that this method cannot be 
practiced at sea. 

248. The grand discovery of the progressive motion 
of light, was first made by observations on the eclipses 
of Jupiter's satellites. In the year 1675, it was remarked 
by Koemer, a Danish astronomer, on comparing together 
observations of these eclipses during many successive 
years, that they take place sooner by about sixteen min- 
utes, (16m. 26s.6) when the earth is on the same side of 
the sun with the planet, than when she is on the oppo- 
site side. This difference he ascribed to the progressive 
motion of light, which takes that time to pass through 
the diameter of the earth's orbit, making the velocity of 
light about 192,000 miles per second. So great a velocity 
startled astronomers at first, and produced some degree 
of distrust of this explanation of the phenomenon ; but 
the subsequent discovery of what is called the aberration 
of light, led to an independent estimation of the velocity 
of light with almost precisely the same result. 



248. How was the progressive motion of light first discovered ? 
Explain the manner of the discovery. How long is light in trav- 
ersing the diameter of the earth's orbit ? What is its velocity 
per second ? How does this agree with that derived from the 
aberration of light ? 

17 



194 THE PLANETS. 

249. Satuen comes next in the series as we recede 
from the sun, and has, like Jupiter, a system within it- 
self, on a scale of great magnificence. In size it is, next 
to Jupiter, the largest of the planets, being 79,000 miles 
in diameter, or about 1,000 times as large as the earth. 
It has likewise belts on its surface and is attended by 
eight satellites. But a still more wonderful appendage 
is its Ring, a broad wheel encompassing the planet at 
a great distance from it. We have already intimated 
that Saturn's system is on a grand scale. As, however, 
Saturn is distant from us nearly 900,000,000 miles, we 
are unable to obtain the same clear and striking views of 
his phenomena as we do of the phenomena of Jupiter, al- 
though they really present a more wonderful mechanism. 

250. Saturn's ring, when viewed with telescopes of a 
high power, is found to consist of two concentric rings, 
separated from each other by a dark space.* Although 
this division of the rings appears to us, on account of 
our immense distance, as only a fine line, yet it is in 
reality an interval of not less than about 1800 miles. 
The dimensions of the whole system are in round num- 
bers as follows : 

Miles. 

Diameter of the planet, - 79,000 

From the surface of the planet to the inner ring, 20,000 

Breadth of the inner ring, - 17,000 

Interval between the rings, - 1,800 

Breadth of the outer ring, - - - - 10,500 

Extreme dimensions from outside to outside, - 1*76,000 

The figure represents Saturn as it appears to a power- 
ful telescope, surrounded by its rings, and having its 
body striped with dark belts, somewhat similar but 



249. Saturn. — State his diameter and volume, number of 
satellites, ring, distance from the sun. 

* A third ring, less luminous than the other two, has recently been 
discovered. 




broader and less strongly marked than those of Jupiter, 
and owing doubtless to a similar cause. That the ring 
is a solid opake substance, is shown by its throwing its 
shadow on the body of the planet on the side nearest 
the sun, and on the other side receiving that of the body. 
From the parallelism of the belts with the plane of the 
ring, it may be conjectured that the axis of rotation of 
the planet is perpendicular to that plane ; and this con- 
jecture is confirmed by the occasional appearance of 
extensive dusky spots on its surface, which when watch- 
ed indicate a rotation parallel to the ring in lOh. 29m. 17s. 
This motion, it will be remarked, is nearly the same with 
the diurnal motion of Jupiter, subjecting places on the 
equator of the planet to a very swift revolution, and 
occasioning a high degree of compression at the poles, 
the equatorial being to the polar diameter in the high 
ratio of 11 to 10. It requires a telescope of high mag- 
nifying powers and a strong light, to give a full and 



250. How is the ring divided by large telescopes ? State the 
several dimensions of Saturn and his rings. Describe the figure. 
How is the ring inferred to be a solid opake substance ? In what 
time does Saturn revolve on his axis ? What figure does this 
give to the planet ? What kind of telescope is required to see 
the phenomena of Saturn to advantage ? 



196 THE PLANETS. 

striking view of Saturn with his rings, and belts, and 
satellites; for we must bear in mind, that in the dis- 
tance of Saturn, one second of angular measurement 
corresponds to 4,000 miles, a space equal to the semi- 
diameter of our globe. But with a telescope of moderate 
powers, the leading phenomena of the ring itself may 
be observed. 

251. Saturn } s ring, in its revolution around the sun, 
always remains parallel to itself. 

If we hold opposite to the eye a circular ring or disk 
like a piece of coin, it will appear as a complete circle 
when it is at right angles to the axis of vision, but when 
oblique to that axis it will be projected into an ellipse 
more and more flattened as its obliquity is increased, 
until, when its plane coincides with the axis of vision, 
it is projected into a straight line. Let us place on the 
table a lamp to represent the sun, and holding the ring 
at a certain distance inclined a little towards the lamp, 
let us carry it round the lamp, always keeping it parallel 
to itself. During its revolution it will twice present its 
edge to the lamp at opposite points, and twice at places 
90° distant from those points, it will present its broadest 
face towards the lamp. At intermediate points, it will 
exhibit an ellipse more or less open, according as it is 
nearer one or the other of the preceding positions. It 
w T ill be seen also that in one half of the revolution the 
lamp shines on one side of the ring, and in the other 
half of the revolution on the other side. Such would 
be the successive appearances of Saturn's ring to a spec- 
tator on the sun ; and since the earth is, in respect to so 
distant a body as Saturn, very near the sun, these ap- 
pearances are presented to us in nearly the same manner 
as though we viewed them from the sun. Accordingly, 
we sometimes see Saturn's rina' under the form of a 



251. How is the position of the ring with respect to itself in 
all parts of its revolution ? How may the various appearances 
of the ring be represented ? 



SATURN. 



197 



broad ellipse, which grows continually more and more 
acute until it passes into a line, and we either lose sight 
of it altogether, or by the aid of the most powerful 
telescopes, we see it as a fine thread of light drawn 
across the disk and projecting out from it on each side. 
As the whole revolution occupies 30 years, and the edge 
is presented to the sun twice in the revolution, this last 
phenomenon, namely, the disappearance of the ring, 
takes place every 15 years. 

252. The learner may perhaps gain a clearer idea of 
the foregoing appearances from the following diagram : 

Fig. 46. 




Let A, B, C, &c. represent successive positions of 
Saturn and his ring in different parts of his orbit, while 
abc represents the orbit of the earth.* Were the ring 
when at and G perpendicular to the line of vision, 
it would be seen by a spectator situated at a or d a 
perfect circle, but being inclined to that line 28° 4', it 
is projected into an ellipse. This ellipse contracts in 
breadth as the ring passes towards its nodes at A and 
E, where, being seen edgewise, it dwindles into a straight 



252. Explain the revolution of the ring by figure 46. 

* It may be remarked by the learner, that these orbits are made so 
elliptical, not to represent the eccentricity of either the earth's or Sat- 
urn's orbit, bnt merely as the projection of circles seen very obliquely. 

11* 



108 THE PLANETS. 

line. From E to G the ring opens again, becomes broad- 
est at G, and again contracts till it becomes a straight 
line at A, and from this point expands till it recovers 
its original breadth at C. These successive appearances 
are all exhibited to a telescope of moderate powers. 
The ring is extremely thin, since the smallest satellite, 
when projected on it, more than covers it. The thick- 
ness is estimated at 100 miles. 

253. Saturn's ring shines wholly by reflected light 
derived from the sun. This is evident from the fact, 
that that side only which is turned towards the snn is 
enlightened ; and it is remarkable, that the illumination 
of the ring is greater than that of the planet itself, but 
the outer ring is less bright than the inner. Although, 
as we have already remarked, we view Saturn's ring 
nearly as though we saw it from the sun, yet the plane of 
the ring produced may pass between the earth and the 
sun, in which case also the ring becomes invisible, the 
illuminated side being wholly turned from us. Thus when 
the ring is approaching its node at E, a spectator at a 
would have the dark side of the ring presented to him. 

It appears, therefore, that there are three causes for 
the disappearance of Saturn's ring ; first, when the edge 
of the ring is presented to the sun ; secondly, when the 
edge is presented to the earth ; and thirdly, when the 
unilluminated side is towards the earth. 

254. /Saturn's ring revolves in its own plane in about 
10^ hours, (lOh. 32 m. 15s.4.) La Place inferred this 
from the doctrine of universal gravitation. He proved 
that such a rotation was necessary, otherwise the matter 



253. Whence does the ring derive its light? What causes 
occasion the disappearance of the ring ? At what intervals do 
these disappearances occur ? 

254. In what time does the ring revolve in its own plane ? 
How was this revolution inferred to exist before it was actually 
observed ? 



SATURN. 199 

of which the ring is composed would be precipitated 
upon its primary. He showed that in order to sustain 
itself, its period of rotation must be equal to the time of 
revolution of a satellite, circulating around Saturn at a 
distance from it equal to that of the middle of the ring, 
which period would be about 10| hours. By means of 
spots in the ring, Dr. Herschel followed the ring in its 
rotation, and actually found its period to be the same as 
assigned by La Place, — a coincidence which beautifully 
exemplifies the harmony of truth. 

255. Although the rings are very nearly concentric 
with the planet, yet recent measurements of extreme 
delicacy have demonstrated, that the coincidence is not 
mathematically exact, but that the center of gravity of 
the rings describes around that of the body a very 
minute orbit. This fact, unimportant as it may seem, is 
of the utmost consequence to the stability of the system 
of rings. Supposing them mathematically perfect in 
their circular form, and exactly concentric with the plan- 
et, it is demonstrable that they would form (in spite of 
their centrifugal force) a system in a state of unstable 
equilibrium, which the slightest external power would 
subvert — not by causing a rupture in the substance of 
the rings — but by precipitating them unbroken on the 
surface of the planet. The ring may be supposed of an 
unequal breadth in its different parts, and as consisting 
of irregular solids, whose common center of gravity does 
not coincide with the center of the figure. Were it not 
for this distribution of matter, its equilibrium would be 
destroyed by the slightest force, such as the attraction 
of a satellite, and the ring would finally precipitate it- 
self upon the planet. 

As the smallest difference of velocity between the 
planet and its rings must infallibly precipitate the rings 



255. Are the rings concentric with the planet? What ad- 
vantage results from this arrangement? How must the rings 
appear when seen from the planets ? 



200 THE PLANETS. 

upon the planet, never more to separate, it follows "either 
that their motions in their common orbit round the sun, 
must have been adjusted to each other by an external 
power, with the minutest precision, or that the rings 
must have been formed about the planet while subject 
to their common orbitual motion, and under the full and 
free influence of all the acting forces. 

The rings of Saturn must present a magnificent spec- 
tacle from those regions of the planet which lie on their 
enlightened sides, appearing as vast arches spanning the 
sky from horizon to horizon, and holding an invariable 
situation among the stars. On the other hand, in the 
region beneath the dark side, a solar eclipse of 15 years 
in duration, under their shadow, must afford (to our 
ideas) an inhospitable abode to animated beings, but ill 
compensated by the full light of its satellites. But we 
shall do wrong to judge of the fitness or unfitness of 
their condition from what we see around us, when, per- 
haps, the very combinations which convey to our minds 
only images of horror may be in reality theatres of the 
most striking and glorious displays of beneficent con- 
trivance. (Sir J. Herschel.) 

256. Saturn is attended by eight satellites, one having 
been recently added to the seven before known * Al- 
though bodies of considerable size, their great distance 
prevents their being visible to any telescopes but such 
as afford a strong light and high magnifying powers. 
The outermost satellite is distant from the planet more 
than thirty times the planet's diameter, and is by far 



256. What is the number of Saturn's satellites? How far 
distant from the planet is the outermost satellite ? Do the sat- 
ellites follow Kepler's third law? Which of the satellites are 
easily seen ? Do they undergo eclipses ? 

* The names of the satellites of Saturn, proceeding outwards, are 
Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, and Japetus. 
Hyperion is the one recentlj T discovered. 



URANUS. 201 

the largest of the whole. It is the only one of the series 
whose theory has been investigated further than suffices 
to verify Kepler's law of the periodic times, which is 
found to hold good here as well as in the system of Ju- 
piter. It exhibits, like the satellites of Jupiter, periodic 
variations of light, which prove its revolution on its axis 
in the time of a sidereal revolution about Saturn. The 
next satellite in order, proceeding inwards, is the one 
recently discovered ; the next is tolerably conspicuous ; 
the three next are very minute, and require pretty power- 
ful telescopes to see them ; while the two interior satel- 
lites, which just skirt the edge of the ring, and move 
exactly in its plane, have never been discovered but 
with the most powerful telescopes which human art has 
yet constructed, and then only under peculiar circum- 
stances. At the time of the disappearance of the rings 
(to ordinary telescopes) they were seen by Sir William 
Herschel with his great telescope, projected along the 
edge of the ring, and threading like beads the thin fibre 
of light to which the ring is then reduced. Owing to 
the obliquity of the ring, and of the orbits of the satel- 
lites to that of their primary, there are no eclipses of 
the satellites, the two interior ones excepted, until near 
the time when the ring is seen edgewise. 

257. Uranus is rarely visible except to the telescope. 
Although his diameter is more than four times that of 
the earth, (35,112 miles,) yet his distance from the sun 
is likewise nineteen times as great as the earth's distance, 
or about 1,800,000,000 miles. His revolution around 
the sun occupies nearly 84 years, so that his position in 
the heavens for several years in succession is nearly 
stationary. His path lies very nearly in the ecliptic, 
being inclined to it less than one degree, (W 28".44.) 



257. Uranus. — State liis diameter — distance from the sun — 
periodic time — inclination of his orbit. How would the sun 
appear from Uranus ? State the history of his discovery. By 



202 THE PLANETS. 

The sun himself when seen from Uranus dwindles al- 
most to a star, subtending as it does an angle of only 
1' 40" ; so that the surface of the sun would appear there 
400 times less than it does to us. 

This planet was discovered by Sir William Herschel 
on the 13th of March, 1781. His attention was attracted 
to it by the largeness of its disk in the telescope ; and 
finding that it shifted its place among the stars, he at 
first took it for a comet, but soon perceived that its orbit 
was not eccentric like the orbits of comets, but nearly 
circular like those of the planets. It was then recog- 
nized as a new member of the planetary system, a con- 
clusion which has been justified by all succeeding ob- 
servations. 

The satellites of Uranus are exceedingly minute ob- 
jects, and visible only to the most powerful telescopes. 
Although the discoverer assigned six satellites to this 
planet, yet only two of the number have, until quite 
recently, been seen by other astronomers. Two more 
have of late been added, and an increasing confidence 
is beginning to be felt that the entire number given by 
Herschel will be identified. These satellites offer re- 
markable, and indeed quite unexpected and unexampled 
peculiarities. Contrary to the unbroken analogy of the 
whole planetary system, the planes of their orbits are 
nearly perpendicular to the ecliptic, being inclined no 
less than 78° 58' to that plane, and in these orbits their 
motions are retrograde ; that is, instead of advancing 
from west to east around their primary, as is the case 
with all the other planets and satellites, they move in 
the opposite direction. With this exception, all the 
motions of the planets, whether around their own axes, 
or around the sun, are from west to east. The sun, him- 



how many satellites is Uranus attended ? What is said of their 
minuteness? What remarkable peculiarities have they? In 
what direction are the motions of all the bodies in the solar 
system ? What does this fact indicate with respect to their origin ? 



NEPTUNE. 203 

self, turns on his axis from west to east ; all the primary 
planets revolve around the sun from west to east ; their 
revolutions on their own axes are also in the same direc- 
tion; all the secondaries, with the single exception 
above mentioned, move about their primaries from west 
to east ; and, finally, such of the secondaries as have 
been discovered to have a diurnal revolution, follow the 
same course. Such uniformity among so many motions, 
could have resulted only from forces impressed upon 
them by the same omnipotent hand ; and few things in 
the creation more distinctly proclaim that God made 
the world. 

258. Neptune is (so far as is known) the last planet 
of the series, being removed from the sun to the im- 
mense distance of nearly 3000 millions of miles. Its 
diameter is a little less than that of Uranus, being 
31,000 miles. It is nearly 60 times as large as the earth. 
It takes 164^ years to go round the sun, or about twice 
as long as Uranus. 

The discovery of this planet (so late as the year 1846) 
was the most remarkable ever made in astronomy. Al- 
though a comparatively large planet, yet it is so far 
from us as to be wholly invisible to the naked eye; and 
yet its existence, the place among the stars where it lay 
hidden, and various other particulars respecting it, were 
determined by Leverrier, a distinguished French astron- 
omer, before it was actually seen. Indeed, he directed, 
from the result of his calculations, to what spot in the 
starry heavens the telescope must be pointed in order to 
see it, and thus it was found. This wonderful result was 
reached in the following manner: It had been observed 
that some unknown cause disturbed the motions of Ura- 
nus, which led astronomers to suspect the existence of a 
planet outside of it. The problem then was to find a 
planet so situated, and of such a size, as would produce 
the effect in question. The principle of gravitation would 
lead to an estimate of the nature, duration, and amount of 
the disturbing force, and this would reveal the position 



204 THE PLANETS. 

and magnitude of the body. To make the estimates so 
accurately as to be able to point the telescope among the 
stars to the precise point where the hidden body lay, 
required great genius and great skill in mathematical 
calculations. The success that crowned the undertaking 
showed that these qualifications were possessed in the 
highest degree by the discoverer, and at the same time 
displayed the wonderful reach of the principle of uni- 
versal gravitation, as well as the boundless resources of 
the higher mathematics. 

THE NEW PLANETS, OR ASTEKOIDS. 

259. The commencement of the present century was 
rendered memorable in the annals of astronomy, by- the 
discovery of four new planets between Mars and Jupiter. 
Kepler, from some analogy which he found to subsist 
among the distances of the planets from the sun, had 
long before suspected the existence of one at this dis- 
tance ; and his conjecture was rendered more probable 
by the discovery of Uranus, which follows the analogy 
of the other planets. So strongly, indeed, were astrono- 
mers impressed with the idea that a planet would be 
found between Mars and Jupiter, that, in the hope of 
discovering it, an association was formed on the conti- 
nent of Europe of twenty-four observers, who divided 
the sky into as many zones, one of which was allotted 
to each member of the association. The discovery of 
the first of these bodies was however made accidentally 
by Piazzi, an astronomer of Palermo, on the first of Jan- 
uary, 1801. It was shortly afterwards lost sight of on 
account of its proximity to the sun, and was not seen 
again until the close of the year, when it was rediscov- 
ered in Germany. Piazzi called it Ceres, in honor of 
the tutelary goddess of Sicily; and her emblem, the ?, 
has been adopted as its appropriate symbol. 



258. Neptune. — State his distance from the sun — diameter — 
periodic time. Relate the historv of his discovery. 



NEW PLANETS. 205 

The difficulty of finding Ceres induced Dr. Olbers, of 
Bremen, to examine with particular care all the small 
stars that lie near her path, as seen from the earth ; and 
while prosecuting these observations, in March, 1802, he 
discovered another similar body, very nearly at the same 
distance from the sun, and resembling the former in 
many other particulars. The discoverer gave to this 
second planet the name of Pallas, choosing for its symbol 
the lance $ , the characteristic of Minerva. 

260. The most surprising circumstance connected 
with the discovery of Pallas, was the existence of two 
planets at nearly the same distance from the sun, and 
apparently having a common node. On account of this 
singularity, Dr. Olbers was led to conjecture that Ceres 
and Pallas are only fragments of a larger planet, which 
had formerly circulated at the same distance, and been 
shattered by some internal convulsion. The hypothesis 
suggested the probability that there might be other frag- 
ments, whose orbits, however they might differ in ec- 
centricity and inclination, might be expected to cross 
the ecliptic at a common point, or to have the same node. 
Dr. Olbers, therefore, proposed to examine carefully 
every month the two opposite parts of the heavens in 
which the orbits of Ceres and Pallas intersect one an- 
other, with a view to the discovery of other planets, 
which might be sought for in those parts with greater 
chance of success than in a wider zone, embracing the 
entire limits of these orbits. Accordingly, in 1804, near 
one of the nodes of Ceres and Pallas, a third planet was 
discovered. This was called Juno, and the character $ 
was adopted for its symbol, representing the starry 
sceptre of the queen of Olympus. Pursuing the same 



259. Name the New Planets. When were they discovered ? 
What had been conjectured previous to their discovery? Who 
discovered the first ? What is its name ? How was Pallas dis- 
covered ? 

18 



206 THE PLANETS. 

researches, in 1807, a fourth planet was discovered, to 
which was given the name of Vesta, and for its symbol 
the character £ was chosen — an altar surmounted with 
a censer holding the sacred fire. 

Since 1845 to the present time, (Nov. 1854,) no fewer 
than 29 more Asteroids have been discovered, making 
the entire number at present 33. Their names are Ceres, 
Pallas, Juno, and Yesta; Astrea, Hebe, Iris, Flora, 
Metis, Hygeia, Parthenope, Victoria, Egeria, Irene, 
Eunomia, Psyche, Thetis, Melpomene, Fortuna, Massa- 
lia, Lutetia, Calliope, Thalia, Themis, Phocea, Proser- 
pina, Euterpe, Bellona, Amphytrite, Urania, Euphro- 
syne, Pomona, Polymnia. 

261. The average distance of these bodies from the 
sun is 261,000,000 miles ; and it is remarkable that their 
orbits are very near together. Taking the distance of 
the earth from the sun for unity, their respective dis- 
tances are 2.77, 2.77, 2.67, 2.37. 

As they are found to be governed, like the other mem- 
bers of the solar system, by Kepler's law, that regulates 
the distances and times of revolution, their periodical 
times are of course pretty nearly equal, averaging about 
4i years. 

In respect to the inclination of their orbits, there is 
considerable diversity. The orbit of Yesta is inclined 
to the ecliptic only about 7°, while that of Pallas is more 
than 34°. They all therefore have a higher inclination 
than the orbits of the old planets, and of course make 
excursions from the ecliptic beyond the limits of the 
Zodiac. 

The eccentricity of their orbits is also, in general, 
greater than that of the old planets ; and the eccentrici- 



260. How do Ceres and Pallas compare in distance from the 
sun and the place of their nodes ? What hypothesis did Olbers 
adopt ? State the circumstances connected with the discovery of 
Juno and Yesta. What additional asteroids have been discovered 
since 3 845 ? 



MOTIONS OF THE PLANETARY SYSTEM. 207 

ties of the orbits of Pallas and Juno exceed that of the 
orbit of Mercury. 

Their small size constitutes one of their most remark- 
able peculiarities. The difficulty of estimating the ap- 
parent diameters of bodies at once so very small and so 
far off, would lead us to expect different results in the 
actual estimates. Accordingly, while Dr. Herschel es- 
timates the diameter of Pallas at only 80 miles, Schroe- 
ter places it as high as 2,000 miles, or about the size of 
the moon. The volume of Yesta is estimated at only 
one fifteen thousandth part of the earth's, and her sur- 
face is only about equal to that of the kingdom of Spain. 
These little bodies are surrounded by atmospheres of 
great extent, some of which are uncommonly luminous, 
and others appear to consist of nebulous or vapory mat- 
ter. These planets in general shine with a more vivid 
light than might be expected from their great distance 
and diminutive size. 



CHAPTER IX. 



MOTIONS OF THE PLANETARY SYSTEM QUANTITY OF MAT- 
TER IN THE SUN AND PLANETS STABILITY OF THE SO- 
LAR SYSTEM. 

262. We have waited until the learner may be sup- 
posed to be familiar with the contemplation of the heav- 
enly bodies, individually, before inviting his attention to 
a systematic view of the planets, and of their motions 
around the sun. The time has now arrived for entering 
more advantageously upon this subject than could have 
been done at an earlier period. 



261. What is the average distance of the New Planets from 
the sun ? How do these orbits lie with respect to each other ? 
Are they subject to Kepler's third law ? What is their average 
periodical time ? What is said of the inclination of their orbits ? 
Also, of the eccentricity ? What is their size ? 



208 THE PLANETS. 

There are two methods of arriving at a knowledge of 
the motions of the heavenly bodies. One is to begin 
with the' apparent, and from these to deduce the real 
motions ; the other is, to begin with considering things 
as they really are in nature, and then to inquire why 
they appear as they do. The latter of these methods is 
by far the more eligible ; it is much easier than the 
other, and proceeding from the less difficult to that which 
is more difficult, from motions that are very simple to 
such as are complicated, it finally puts the learner in 
possession of the whole machinery of the heavens. We 
shall, in the first place, therefore, endeavor to introduce 
the learner to an acquaintance with the simplest motions 
of the planetary system, and afterwards to conduct him 
gradually through such as are more complicated and 
difficult. 

263. Let us first of all endeavor to acquire an adequate 
idea of absolute space, such as existed before the crea- 
tion of the world. We shall find it no easy matter to 
form a correct notion of infinite space ; but let us fix our 
attention, for some time, upon extension alone, devoid 
of every thing material, without light or life, and with- 
out bounds. Of such a space we could not predicate 
the ideas of up or down, east, west, north, or south, but 
all reference to our own horizon (which habit is the most 
difficult of all to eradicate from the mind) must be com- 
pletely set aside. Into such a void we would introduce 
the Sun. We would contemplate this body alone, in 
the midst of boundless space, and continue to fix the at- 
tention upon this subject, until we had fully settled its 
relations to the surrounding void. The ideas of up and 
down would now present themselves, but as yet there 
would be nothing to suggest any notion of the cardinal 



262. What are the two methods of studying the motions of 
the heavenly bodies ? Which method is best ? What motions 
will be first considered ? 



MOTIONS OF THE PLANETARY SYSTEM. 209 

points. We suppose ourselves next to be placed on the 
surface of the sun, and the firmament of stars to be 
lighted np. The slow revolution of the sun on his axis, 
would be indicated by a corresponding movement of 
the stars in the opposite direction; and in a period equal 
to more than 25 of our days, the spectator would see 
the heavens perform a complete revolution around the 
sun, as he now sees them revolve around the earth once 
in 21 hours. The point of the firmament where no mo- 
tion appeared, would indicate the position of one of the 
poles, which being called North, the other cardinal 
points would be immediately suggested. 

Thus prepared, we may now enter upon the consider- 
ation of the planetary motions. 

264:. Standing on the sun, we see all the planets mo- 
ving slowly around the celestial sphere, nearly in the 
same great highway, and in the same direction from 
west to east. They move, however, with very unequal 
velocities. Mercury makes very perceptible progress 
from night to night, like the moon revolving about the 
earth, his daily progress eastward being one third as 
great as that of the moon, since he completes his entire 
revolution in about three months.. If we watch the 
course of this planet from night to night, we observe it, 
in its revolution, to cross the ecliptic in two opposite 
points of the heavens, and wander about 7° from that 
plane at its greatest distance from it. Knowing the po- 
sition of the orbit of Mercury with respect to the ecliptic, 
we may now, in imagination, represent that orbit by a 
great circle passing through the center of the planet and 
the center of the sun, and cutting the plane of the eclip- 
tic in two opposite points at an angle of 7°. We may 



263. How can we form a correct idea of absolute space? 
What can we predicate of such a space ? If the sun were placed 
in such a void, what new ideas would present themselves ? How 
should we get a knowledge of the cardinal points ? 

18* 



210 THE PLANETS. 

imagine the intersection of these two great circles with 
the celestial vault to be marked out in plain and palpa- 
ble lines on the face of the sky ; but we must bear in 
mind that these orbits are mere mathematical planes, 
having no permanent existence in nature, any more than 
the path of an eagle flying through the sky ; and if we 
conceive of their orbits marked on the celestial vault, 
we must be careful to attach to the representation the 
same notion as to a thread or wire, carried round to 
trace out the course pursued by a horse in a race-ground.* 
The planes of both the ecliptic and the orbit of Mer- 
cury, may be conceived of as indefinitely extended to a 
great distance until they meet the sphere of the stars ; 
but the lines which the earth and Mercury describe in 
those planes, that is, their orbits, may be conceived of as 
comparatively near to the sun. Could we now for a 
moment be permitted to imagine that the planes of the 
ecliptic, and of the orbit of Mercury, were made of thin 
plates of glass, and that the paths of the respective plan- 
ets were marked out on their planes in distinct lines, we 
should perceive the orbit of the earth to be almost a per- 
fect circle, while that of Mercury would appear distinctly 
elliptical. But having once made use of a palpable sur- 
face and visible lines to aid us in giving position and 



264. Where must the spectator be placed in order to see the 
real motions of the planets? How would the motions of the 
several planets appear from this station? State the particular 
movements of Mercury. How may we imagine the ecliptic and 
the orbit of Mercury to be represented on the sky ? How shall 
we conceive of the planes of these orbits as distinguished from 
the orbit itself? 



* It would seem superfluous to caution the reader on so plain a point, 
did not the experience of the instructor constantly show that young 
learners, from the habit of seeing the celestial motions represented in 
orreries and diagrams, almost always fall into the absurd notion of con- 
sidering the orbits of the planets as having a distinct and independent 
existence. 



MOTIONS OF THE PLANETARY SYSTEM. 211 

figure to the planetary orbits, let us now throw aside 
these devices, and hereafter conceive of these planes 
and orbits as they are in nature, and learn to refer a 
body to a mere mathematical plane, and to trace its 
path in that plane through absolute space. 

265. A clear understanding of the motions of Mer- 
cury and of the relation of its orbit to the plane of the 
ecliptic, will render it easy to understand the same -par- 
ticulars in regard to each of the other planets. Standing 
on the sun, we should see each of the planets pursuing a 
similar course to that of Mercury, all moving from west 
to east, with motions differing from each other chiefly 
in two respects, namely, in their velocities, and in the 
distances to which they ever recede from the ecliptic. 

The earth revolves about the sun very much like Ve- 
nus, and to a spectator on the sun, the motions of these 
two planets would exhibit much the same appearances. 
We have supposed the observer to select the plane of 
the earth's orbit as his standard of reference, and to see 
how each of the other orbits is related to it ; but such a 
selection of the ecliptic is entirely arbitrary ; the spec- 
tator on the sun, who views the motions of the planets 
as they actually exist in nature, would make no such 
distinction between the different orbits, but merely in- 
quire how they were mutually related to each other. 
Taking, however, the ecliptic as the plane to which all 
the others are referred, we do not, as in the case of the 
other planets, inquire how its plane is inclined, nor 
what are its nodes, since it has neither inclination nor 
node. 

266. The attempt to exhibit the motions of the solar 
system, and the positions of the planetary orbits by 



265. If we stood on the sun, how should we see each of the 
planets revolve ? Why is the earth's orbit selected as the stan- 
dard of reference ? Would the spectator on the sun make any 
such distinction ? 



212 THE PLANETS. 

means of diagrams, or even orreries, is usually a failure. 
The student who relies exclusively on such aids as these, 
will acquire ideas on this subject that are both inade- 
quate and erroneous. They may aid reflection, but can 
never supply its place. The impossibility of represent- 
ing things in their just proportions will be evident wdien 
we reflect, that to do this, if, in an orrery, we make 
Mercury as large as a cherry, we should require to re- 
present the sun by a globe six feet in diameter. If w T e 
preserve the same proportions in regard to distance, we 
must place Mercury 250 feet, and Neptune more than 
five miles from the sun. The mind of the student of 
astronomy must, therefore, raise itself from such imper- 
fect representations of celestial phenomena as are afford- 
ed by artificial mechanism, and, transferring his contem- 
plations to the celestial regions themselves, he must con- 
ceive of the sun and planets as bodies that bear an in- 
significant ratio to the immense spaces in which they 
circulate, resembling more a few little birds flying in 
the open sky, than they do the crowded machinery of 
an orrery. 

267. Having acquired as correct an idea as we are 
able of the planetary system, and of the positions of the 
orbits with respect to the ecliptic, let us next inquire 
into the nature and causes of the apparent motions. 

The apparent motions of the planets are exceedingly 
unlike the real motions, a fact which is owing to two 
causes ; first, we mew them out of the center of their Dr- 
oits ; secondly, we are ourselves in motion. From the 
first cause, the apparent places of the planets are greatly 
changed by perspective ; and from the second cause, 
w j e attribute to the planets changes of place which arise 
from our own motions, of which we are unconscious. 



266. What is said of the attempt to represent the positions 
and motions of the solar system by diagrams and orreries ? Give 
examples. 



MOTIONS OF THE PLANETARY SYSTEM. 213 

The situation of a heavenly body as seen from the 
center of the sim is called its heliocentric place; as seen 
from the center of the earth, its geocentric place. The 
geocentric motions of the planets must, according to 
what has just been said, be far more irregular and com- 
plicated than the heliocentric. 

268. The apparent motions of the Inferior Planets as 
seen from the earth, have been already explained in ar- 
ticles 216 and 217 ; from which it appeared, that Mer- 
cury and Yenus move backwards and forwards across 
the sun, the former never being seen farther than 29°, 
and the latter never more than 47° from that luminary. 
It was also shown that while passing from the greatest 
elongation on one side to the greatest elongation on the 
other side, through the superior conjunction, the appa- 
rent motions of these planets are accelerated by the mo- 
tion of the earth ; but that while moving through the 
inferior conjunction, at which time their motions are 
retrograde, they are apparently retarded by the earth's 
motion. Let us now see what are the geocentric mo- 
tions of the Superior Planets. 

269. Let A, B, C, (Fig. 47), represent the earth in 
different positions in its orbit, and M a superior planet 
as Mars, and NR, an arc of the concave sphere of the 
heavens. First, suppose the planet to remain at rest in 
M, and let us see what apparent motions it will receive 
from the real motions of the earth. When the earth is 
at B, it will see the planet in the heavens at N" ; and as 
the earth moves successively through C, D, E, F, the 
planet will appear to move through O, P, Q, R. B and 



267. Are the apparent motions of the planets like the real 
motions ? What- makes them different ? How does each cause 
operate ? What is the heliocentric place, and what the geocen- 
tric place of a planet ? 

268. Describe the apparent motions of Mercury and Venus 
from figure 40. 



214 



THE PLANETS. 



F are the two points of greatest elongation of the earth 
from the sun as seen from the planet ; hence between 
these two points, while passing through the part of her 
orbit most remote from the planet, (when the planet is 
seen in superior conjunction,) the earth by her own mo- 
Fig. 47. 




tion gives an apparent motion to the planet in the order 
of the signs — that is, the apparent motion given by the 
earth is direct. But in passing from F to B through A, 
when the planet is seen in opposition, the apparent mo- 
tion given to the planet by the earth's motion is from 
R to S", and is therefore retrograde. As the arc described 



269. Describe the motions of the Superior Planets from fig- 
ure 47. The planet remaining at rest, what apparent motions 
will the motion of the earth impart to it, when in opposition ? 
What when in superior conjunction ? 



MOTIONS OF THE PLANETARY SYSTEM. 215 

by the earth, when the motion is direct, is much greater 
than when the motion is retrograde, while the apparent 
arc of the heavens described by the planet from N to E 
in the one case, and from K to N in the other, is the same 
in both cases, the retrograde motion is much swifter 
than the direct, being performed in much less time. 

270. But the superior planet is not in fact at rest, as 
we have supposed, but is all the while moving east- 
ward, though with a slower motion than the earth. In- 
deed, with respect to the remotest planets, as Saturn and 
Uranus, the forward motion is so exceedingly slow that 
the above representation is nearly true for a single year. 
Still, the effect of the real motions of all the superior 
planets eastward, is to increase the direct apparent mo- 
tion communicated by the earth and to diminish the 
retrograde motion. 

If Mars stood still while the earth went round the 
sun, then a second opposition as at A, would occur at 
the end of one year from the first ; but while the earth 
is performing this circuit, Mars is also moving the same 
way, more than half as fast, so that when the earth re- 
turns to A, the planet has already performed more than 
half the same circuit, and will have completed its whole 
revolution before the earth comes up with it. Indeed, 
Mars, after having been once seen in opposition, does 
not come into opposition again until after two years and 
fifty days. And since the planet is then comparatively 
very near to us, and appears very large and bright, rising 
unexpectedly about the time the sun sets, he surprises 
the world as though it were some new celestial body. 
But on account of the slow progress of Saturn and Ura- 
nus, we find, after having performed one circuit around 
the sun, that they are but little advanced beyond where 
we left them at. the last opposition. The time between 
one opposition of Saturn and another is only a year and 
thirteen days. 

It appears, therefore, that the superior planets steadily 
pursue their course around the sun, but that their appa- 



216 THE PLANETS. 

rent retrograde motion when in opposition is occasioned 
by our passing by them with a swifter motion, like the 
apparent backward motion of a vessel when we over- 
take it and pass rapidly by it in a steamboat. 

QUANTITY OF MATTER IN THE SUN AND PLANETS. 

271. It would seem at first view very improbable that 
an inhabitant of this earth should be able to weigh the 
sun and planets, and estimate the exact quantity of mat- 
ter which they severally contain. But the principles of 
Universal Gravitation conduct us to this result, by a 
process remarkable for its simplicity. By comparing the 
relations of a few elements that are known to us, we 
ascend to the knowledge of such as appeared to be be- 
yond the pale of human investigation. We learn the 
quantity of matter in a body from the force of gravity it 
exerts, and this force is estimated by its effects. Hence 
worlds are weighed with as much ease as a pebble or an 
article of merchandise. 

272. The sun contains about 355,000 times as much 
matter as the earth, and 800 times as much matter as 
all the planets. This, however, is owing rather to its 
great size than to the specific gravity of its materials, 
for the density of the sun is only one fourth as great as 
that of the earth. The earth is nearly 5 \ times as heavy 
as water, but the sun is only a little heavier than that 
fluid. The planets near the sun are in general more 
dense than those more remote ; Mercury being as heavy 



270. How does the real motion of the planet modify the fore- 
going results ? How in respect to the remotest planets, as Ura- 
nus, and how in respect to a nearer planet, as Mars ? How often 
is Mars in opposition ? "What is his appearance then ? 

271. What is said of the apparent difficulty of weighing the 
sun and planets ? What great principles lead us to this result ? 
How do we learn the quantity of matter in the bodies of the 
solar system ? 



STABILITY OF THE SOLAR SYSTEM. 21*7 

as iron ore, while Saturn is as light as cork. The de- 
crease in density, however, is not entirely regular, since 
Venus is a little lighter than the earth, while Jupiter is 
heavier than Mars, and Uranus than Saturn. 

STABILITY OF THE SOLAR SYSTEM. 

273. The perturbations or irregularities occasioned in 
the motions of the planets by their action on each other, 
are very numerous, since every body in the system ex- 
erts an attraction on every other, in conformity with the 
law of Universal Gravitation. Yenus and Mars, ap- 
proaching as they do at times comparatively near to the 
Earth, sensibly disturb its motions ; and Jupiter and 
Saturn, although very far asunder, still, in consequence 
of their great masses, exert on each other, when on the 
same side of the heavens especially, a decided influence. 
Moreover the Sun, by his unequal action on the several 
planets, in consequence of the peculiar figure of each, 
produces various irregularities in their motions. These 
perturbations are divided into periodical and secular: 
periodical, when completed in comparatively short 
periods, as those for example which undergo all their 
changes during one revolution of the planet ; and secu- 
lar, when completed only in very long periods, as those 
which affect the form and inclination of the orbits. 

274. If the only bodies in the system were a central 



272. How much more matter does the sun contain than the 
earth? How much more than all the planets? What is the 
density of the sun compared with that of the earth ? How much 
heavier is the earth than water? How much heavier is the sun 
than water ? Which of the planets have the greatest density ? 
How heavy is Mercury ? How heavy is Saturn ? 

273. To what extent do perturbations exist among the planets ? 
What is their cause? "What planets in particular disturb the 
motions of the earth ? In what way does the sun disturb the sev- 
eral planets ? State the distinction between periodical and secu- 
lar perturbations. 

19 



218 THE PLANETS. 

body like the Sun, and a revolving body like Venus, 
then when the planet was once pnt in motion with such 
a projectile force as to make it describe an ellipse, it 
would forever continue to describe the same figure with- 
out the least variation ; but now introduce a third body 
so near as to exert on it a decided attraction, and its 
motions no longer retain their simplicity, but become 
complicated by the conflicting influences of the two at- 
tracting bodies. The Sun, however, in consequence of 
its mass, which is eight hundred times as great as that 
of all the planets, and of course vastly greater than any 
one of them, exerts a force so much superior to that of 
any or all the other disturbing bodies, that the elliptical 
figure of the orbit is nearly maintained, and a mere ap- 
proximation to the place of the planet is obtained, by 
neglecting all those minor forces, and simply contem- 
plating it as revolving in an elliptical orbit. Still it is 
e c sential, in order to find the exact place of a planet at 
any given time, that all these irregularities, minute as 
they may be, should be carefully summed up, and their 
resultant applied to the elliptical motion. To inves- 
tigate these perturbations, to estimate their precise 
amount, and to register them in tables, for the use of 
the practical astronomer, have constituted a large part 
of the labors of modern astronomy. The knowledge 
gained by astronomers of the planetary motions, con- 
sidering the very numerous irregularities, both perio- 
dical and secular, to which they are subject, is truly 
wonderful. The motion of Jupiter, for instance, is so 
perfectly calculated, that astronomers have computed, 
ten. years beforehand, the time at which it will pass 
the meridian of different places, and the result does not 
vary half a second from the prediction. The more ob- 
vious irregularities have been detected by observation ; 
the more minute, by following out the consequences of 
universal gravitation. Even those at first revealed to 
the instruments of the astronomer, have been confirmed 
and estimated with greater accuracy, by the same far- 
reaching principle ; and many of the irregularities have 



STABILITY OF THE SOLAR SI STEM. 219 

been first brought to light by this theory, which had 
before eluded observation ; although when once pointed 
out as a result of the principle of gravitation, careful 
instrumental measurements have confirmed them, ex- 
cept in cases where the force was too minute to be 
reached by the most refined observation. Periodical 
perturbations among the bodies of the solar system, may 
be compared to the regular flux and reflux of the tides, 
by which the ocean daily oscillates about its mean level ; 
while secular perturbations would resemble any slow 
changes of level, which, accumulating from time to 
time, might finally become obvious to measures of the 
depth of the ocean, as recorded from age to age. As an 
example of the extreme minuteness of some of these 
secular perturbations, we may instance the changes in 
the eccentricity of the Earth's orbit. The entire eccen- 
tricity is so small, that the figure when drawn on paper 
in just proportions, can scarcely be distinguished from 
a circle, the focus of the ellipse being distant from the 
center only about ¥ V part of the semi-major axis; but 
the change of eccentricity in a century is only one 
twenty-five thousandth part of this small quantity. 

275. But although the secular inequalities of the 
planetary motions are exceedingly slow, yet may they 
not in time accumulate so as to derange the whole sys- 
tem ; and do they not at least indicate that the system 



274. If there were only a central body, as the Sun, and revolv- 
ing body, as Yenus, how would the planet move \ Consequence 
of introducing a third body ? What effect has the greater mass 
of the sun in preserving the stability of the planetary motions ? 
AVhat is necessary in order to find the exact place of a planet ? 
What has constituted a large part of the labors of modern astro- 
nomers ? What' is said of the accuracy to which astronomical 
calculations are brought ? How were these irregularities detect- 
ed ? To what are periodical and secular perturbations respective- 
ly compared \ What is said of the change of eccentricity in the 
earth's orbit ? 



220 THE PLANETS. 

carries within it the seeds of its own dissolution ? So 
far is this from being the case, that the stability of the 
solar system is a fact established on the most unques- 
tionable evidence. Even a superficial view of the sys- 
tem, will convince us that care has been bestowed on 
this point by several obvious arrangements. One is, 
that the planets have severally so small masses com- 
pared with the sun, as to interfere but little with his 
supremacy over the planetary motions. Another is, 
that the planets are placed at such great distances from 
each other — a distance which is greater among the 
larger bodies, as Jupiter and Saturn, than among the 
smaller, as the Earth and Yenus ; and another still, that 
the orbits are less eccentric when the masses are greater, 
by which provision they are always maintained at a 
remote distance from the sun. Were the orbit of Jupi- 
ter as eccentric as that of Mars, he would approach so 
near the earth at his perihelion, as greatly to endanger 
its stability. The major axes of the planetary orbits 
remain from year to year constantly of the same length, 
by which means the periodic times (which are always 
in a fixed mathematical ratio to the major axes), remain 
invariable, else we should have years of different lengths ; 
but the nicest observations can detect no difference in 
the times in which the planets severally perform their 
revolutions about the sun. 

276. It is worthy of remark, as evincing the super- 
intending care of Providence, that those perturbations, 
such as changes in the place of the perihelion, affecting 
a change of direction in space of the major axis of the 
orbit, or in the place of the nodes, which, by accumu- 
lating do not endanger the stability of the system, pro- 
ceed onward through the entire circuit of the heavens, 
while perturbations which, by indefinite accumulation, 



275. What planets have orbits of small eccentricity? How 
does this fact contribute to the stability of the system ? State 
the conditions necessary to the stability of the system. 



COMETS. 221 

would bring ruin to the system, such as variations of 
eccentricity and of inclination, are not progressive but 
oscillatory, waving to and fro within the limits of entire 
safety. These ends would not have been secured, had 
the system been constructed differently from what it is. 
Numerous conditions must concur in order to produce 
these results : the mass of the sun must have greatly ex- 
ceeded that of any or all of the planets ; the eccentrici- 
ties of the orbits, and their inclinations, must have been 
small ; and the planets must all have revolved around 
the sun in the same direction. So perfectly, indeed, are 
the planets adjusted to each other, and so beautiful and 
harmonious an order pervades the solar system, that the 
velocities, distances, periodic times, and force of attrac- 
tion towards the slid, of the entire collection of bodies, 
constitute a series in geometrical progression of which 
the first term is the ratio. Thus the comparative dis- 
tance is the square of the velocity, the periodic time is 
the cube, and the attraction towards the sun is the biquad- 
rate. If, for example, we observe that a new-discovered 
body moves 6 times as slow as the earth, we know at 
once that it is 36 times as far from the sun, revolves in 
its orbit in 216 years, and is attracted towards the sun 
1296 times less than the earth is ; and if any one of these 
particulars be given, all the others may in like manner 
be readily found. 



CHAPTER X. 

OF COMETS AND METEORIC SHOWERS. 

277. A Comet, when perfectly formed, consists of 
three parts, the ISTucleus, the Envelope, and the Tail. 
The Nucleus^ or body of the comet, is generally distin- 
guished by its forming a bright point in the center of 
the head, conveying the idea of a solid, or at least of a 
very dense portion of matter. Though it is usually ex- 

19* 



222 co me is. 

ceedingly small when compared with the other parts of 
the comet, yet it sometimes subtends an angle capable 
of being measured by the telescope. The Envelope 
(sometimes called the coma) is a dense nebulous cover- 
ing, which frequently renders the edge of the nucleus 
so indistinct, that it is extremely difficult to ascertain its 
diameter with any degree of precision. Many comets 
have no nucleus, but present only a nebulous mass ex- 
tremely attenuated on the confines, but gradually in- 
creasing in density towards the center. Indeed, there 
is a regular gradation of comets, from such as are com- 
posed merely of a gaseous or vapory medium, to those 
which have a well-defined nucleus. In some instances 
on record, astronomers have detected with their tele- 
scopes small stars through the densest part of a comet. 

The Tail is regarded as an expansion or prolongation 
of the coma ; and presenting, as it sometimes does, a 
train of appalling magnitude, and of a pale, disastrous 
light, it confers on this class of bodies their peculiar 
celebrity. 

Fig. 48. 




These several parts are exhibited in figure 48, which 
represents the appearance of the comet of 1680. 



2*1*1. Of what three parts does a comet consist ? Describe each. 



COMETS, 223 

278. The number of comets belonging to the solar 
system, is probably very great. Many, no doubt, escape 
observation by being above the horizon in the daytime. 
Seneca mentions, that during a total eclipse of the sun, 
which happened 60 years before the Christian era, a 
large and splendid comet suddenly made its appearance, 
being very near the sun. The elements of at least 
180 comets have been computed, and arranged in a cat- 
alogue for comparison. Of these, six are particularly 
remarkable, viz. the comets of 1680, 1770, and 1843; 
and those which bear the names of ITalley, Encke, and 
Biela. The comet of 1680 was distinguished not only 
for its astonishing size and splendor, but is remarkable 
for having been the first comet whose elements were 
determined on the sure basis of mathematics, as was 
done by Sir Isaac ]N"ewton, it having appeared in his 
time. The comet of 1770 is memorable for the changes 
its orbit has undergone by the action of Jupiter, and for 
having approached very near to the earth. The comet 
of 1843 was the most remarkable in its appearance of 
all that have been seen in modern times, having been 
visible at noon-day. ITalley's comet (the same which 
reappeared in 1835) is distinguished as that whose re- 
turn was first successfully predicted, and whose orbit 
was first accurately determined ; and Biela's and 
Encke's comets are well known for their short periods 
of revolution, which subject them frequently to the view 
of astronomers. Biela's comet, at its return in 1846, 
displayed another remarkable feature — a separation into 
two distinct parts. At one time the distance of one nu- 
cleus from the other, was estimated at 157,000 miles. 

279. In magnitude and brightness comets exhibit a 
great diversity. History informs us of comets so bright 



278. What is said of the number of comets ? How many have 
been arranged in a table ? Specify the six that are most remark- 
able. State particulars respecting each. 



224 COMETS. 

as to be distinctly visible in the daytime, even at noon 
and in the brightest sunshine, — a fact regarded as almost 
incredible, until verified in the great comet of 1843. 
Such was the comet seen at Rome a little before the 
assassination of Julius Csesar. The comet of 1680 cover- 
ed an arc of the heavens of 97°, and its length was esti- 
mated at 123,000,000 miles. That of 1811 had a nucleus 
of only 428 miles in diameter, but a tail 132,000,000 miles 
long. Had it been coiled around the earth like a serpent, 
it would have reached round more than 5,000 times. 
Other comets are of exceedingly small dimensions, the 
nucleus being estimated at only 25 miles ; and some 
which are destitute of any perceptible nucleus, appear 
to the largest telescopes, even when nearest to us, only 
as a small speck of fog, or as a tuft of down. The ma- 
jority of comets can be seen only by the aid of the tel- 
escope. 

The same comet, indeed, has often very different as- 
pects at its different returns. Halley's comet in 1305 
was described by the historians of that age, as the comet 
of terrific magnitude, (cometa horrendm magnitudinis /) 
in 1456 its tail reached from the horizon to the zenith, 
and inspired such terror, that by a decree of the Pope 
of Rome, public prayers were offered up at noon-day in 
all the Catholic Churches to deprecate the wrath of 
heaven, while in 1682, its tail was only 30° in length, 
and in 1759 it was visible only to the telescope, until 
after it had passed the perihelion. At its recent return 
in 1835, the greatest length of the tail was about 12°. 
These changes in the appearance of the same comet, 
are partly owing to the different positions of the earth 
with respect to them, being sometimes much nearer to 
them when they cross its track than at others ; also one 



279. What is said of the magnitude and brightness of comets 1 
What was the length of the comet of 1680? Ditto of 1811 ? 
Has the same comet different aspects at different returns ? Ex- 
ample in Halley's comet. 



COMETS. 225 

spectator so situated as to see the coma at a higher angle 
of elevation or in a purer sky than another, will see the 
train longer than it appears to another less favorably 
situated ; but the extent of the changes are such as indi- 
cate also a real change in magnitude and brightness. 

280. The periods of comets in their revolutions around 
the sun are equally various. Encke's comet, which has 
the shortest known period, completes its revolution in 
3^- years, or more accurately, in 1208 days ; while that 
of 1811 is estimated to have a period of 3383 years. 

281. The distances to which different comets recede 
from the sun, are also very various. While Encke's 
comet performs its entire revolution within the orbit of 
Jupiter, Halley's comet recedes from the sun to twice 
the distance of Uranus, or nearly 3600,000,000 miles. 
Some comets, indeed, are thought to go to a much 
greater distance from the sun than this, while some even 
are supposed to pass into parabolic or hyperbolic orbits, 
and never to return. 

282. Comets shine hy reflecting the light of the sun. 
In one or two instances they have exhibited distinct 
phases, although the nebulous matter with which the 
nucleus is surrounded, would commonly prevent such 
phases from being distinctly visible, even when they 
would otherwise be apparent. Moreover, certain quali- 
ties of polarized light enable the optician to decide 
whether the light of a given body is direct or reflected ; 
and M. Arago, of Paris, by experiments of this kind on 



280. How are the periods of comets ? What is that 'of Encke's 
comet, and that of the comet of 1811 ? 

281. How are the distances of comets from the sun ? Compai e 
Encke's and Halley's. Do comets always return to the sun ? 

282. Do comets shine by direct or by reflected light? Do 
they exhibit phases ? How is it known that their light is reflect- 
ed and not direct light ? 



226 COMETS. 

the light of the comet of 1819, ascertained it to be re- 
flected light. 

283. The tail of a comet usually increases very much 
as it approaches the sun ; and it frequently does not 
reach its maximum until after the perihelion passage. 
In receding from the sun, the tail again contracts, and 
nearly or quite disappears before the body of the comet 
is entirely out of sight. The tail is frequently divided 
into two portions, the central parts, in the direction of 
the axis, being less bright than the marginal parts. In 
1744, a comet appeared which had six tails, spread out 
like a fan. 

The tails of comets extend in a direct line from the 
sun, although more or less curved, like a long quill or 
feather, being convex on the side next to the direction 
in which they are moving, a figure which may result 
from the less velocity of the portions most remote from 
the sun. Expansions of the Envelope have also been 
at times observed on the side next the sun, but these 
seldom attain any considerable length. 

284. The quantity of matter in comets is exceedingly 
small. Their tails consist of matter of such tenuity that 
the smallest stars are visible through them. They can 
only be regarded as great masses of thin vapor, suscep- 
tible of being penetrated through their whole substance 
by the sunbeams, and reflecting them alike from their 
interior parts and from their surfaces. It appears, per- 
haps, incredible that so thin a substance should be visi- 
ble by reflected light, and some astronomers have held 
that the matter of comets is self-luminous ; but it re- 
quires but very little light to render an object visible 
in the night, and a light vapor may be visible when 
illuminated throughout an immense stratum, which 



283. How are the tails of comets affected by being near the 
sun ? How many tails have some comets ? In what direction is 
the tail in respect to the sun ? 



COMETS. 227 

could not be seen if spread over the face of the sky like 
a thin cloud. From the extremely small quantity of 
matter of these bodies, compared with the vast spaces 
they cover, Newton calculated that if all the matter con- 
stituting the largest tail of a comet, were to be com- 
pressed to the same density with atmospheric air, it 
would occupy no more than a cubic inch. This is in- 
credible, but still the highest clouds that float in our 
atmosphere, must be looked upon as dense and massive 
bodies, compared with the filmy and all but spiritual 
texture of a comet. 

285. The small quantity of matter in comets is proved 
by the fact, that they have sometimes passed very near 
to some of the planets, without disturbing their motions 
in any appreciable degree. Thus the comet of 1770, in 
its way to the sun, got entangled among the satellites of 
Jupiter, and remained near them four months, yet it 
did not perceptibly change their motions. The same 
comet also came very near the earth ; so near, that had 
its mass been equal to that of the earth, it would have 
caused the earth to revolve in an orbit so much larger 
than at present, as to have increased the length of the 
year 2h. 47m. Yet it produced no sensible effect on 
the length of the year, and therefore its mass, as is shown 
by La Place, could not have exceeded ^Vo °f that of 
the earth, and might have been less than this to any ex- 
tent. It may indeed be asked, what proof we have that 
comets have any matter, and are not mere reflections of 
light. The answer is, that, although they are not able 
by their own force of attraction to disturb the motions 
of the planets, yet they are themselves exceedingly dis- 
turbed by the action of the planets, and in exact con- 



284. How is the quantity of matter in comets? Of what do 
the tails consist ? Can a substance so thin shine by reflected light % 
What opinion had Newton of the extreme tenuity of the material 
of comets' tails? 



228 COMETS. 

formity with the law of universal gravitation. A deli- 
cate compass may be greatly agitated by the vicinity 
of a mass of iron, while the iron is not sensibly affected 
by the attraction of the needle. 

286. By approaching very near to a large planet, a 
comet may have its orbit entirely changed. This fact 
is strikingly exemplified in the history of the comet of 
1770. At "its appearance in 1770, its orbit was found 
to be an ellipse, requiring for a complete revolution only 
5§ years ; and the wonder was, that it had not been seen 
before, since it was a very large and bright comet. As- 
tronomers suspected that its path had been changed, and 
that it had been recently compelled to move in this short 
ellipse, by the disturbing force of Jupiter and his satel- 
lites. The French Institute, therefore, offered a high 
prize for the most complete investigation of the elements 
of this comet, taking into account any circumstances 
which could possibly have produced an alteration in its 
course. By tracing back the movements of this comet 
for some years previous to 1770, it was found that, at 
the beginning of 1767, it had entered considerably 
within the sphere of Jupiter's attraction. Calculating 
the amount of this attraction from the known proximity 
of the two bodies, it was found what must have been its 
orbit previous to the time when it became subject to 
the disturbing action of Jupiter. The result showed 
that it then moved in an ellipse of greater extent, having 
a period of 50 years, and having its perihelion instead 
its aphelion near Jupiter. It was therefore evident why, 
as long as it continued to circulate in an orbit so far 
from the center of the system, it was never visible from 
the earth. In January, 1767, Jupiter and the comet 



285. How is the small quantity of matter in comets proved ? 
How was this indicated by the comet of 1770? What did its 
quantity of matter not exceed as compared with the earth's ? 
May we not infer that they have no matter? 



ORBITS AND MOTIONS OF COMETS. 229 

happened to be very near one another, and as both were 
moving in the same direction, and nearly in the same 
plane, they remained in the neighborhood of each other 
for several months, the planet being between the comet 
and the snn. The consequence was, that the comet's 
orbit was changed into a smaller ellipse, in which its 
revolution was accomplished in 5-J- years. But as it was 
approaching the sun in 1779, it happened again to fall 
in with Jupiter. It was in the month of June, that the 
attraction of the planet began to have a sensible effect ; 
and it was not until the month of October following, 
that they were finally separated. 

At the time of their nearest approach, in August, Ju- 
piter was distant from the comet only T ^ T of its distance 
from the sun, and exerted an attraction upon it 225 
times greater than that of the sun. By reason of this 
powerful attraction, Jupiter being farther from the sun 
than the comet, the latter was drawn out into a new 
orbit, w T hich even at its perihelion came no nearer to 
the sun than the planet Ceres. In this third orbit, the 
comet requires about 20 years to accomplish its revolu- 
tion ; and being at so great a distance from the earth, it 
is invisible, and will forever remain so, unless, in the 
course of ages, it may undergo new perturbations, and 
move again in some smaller orbit as before. 

ORBITS AND MOTIONS OF COMETS. 

287. The planets, as we have seen (with the excep- 
tion of the four new ones, which seem to be an inter- 
mediate class of bodies between planets and comets), 



286. How may a comet have its orbit changed? How was 
the orbit of the comet of 17*70 changed? How was this fact 
ascertained? What action did Jupiter exert upon it in 1767, 
and again in 1779? How far was Jupiter from the comet at 
the time of their nearest approach ? How many years does it 
now require to perform its revolution ? 

20 



230 COMETS. 

move in orbits which are nearly circular, and all very 
near to the plane of the ecliptic, and all move in the 
same direction, from west to east. But the orbits of 
comets are far more eccentric than those of the planets ; 
they are inclined to the ecliptic at various angles, being 
sometimes even nearly perpendicular to it ; and the mo- 
tions of comets are sometimes retrograde. 

288. The Elements of a comet are five, viz. (1) The 
perihelion distance / (2) longitude of the perihelion • 
(3) longitude of the node / (4) inclination of the orbit ; 
(5) time of the perihelion passage. 

The investigation of these elements is a problem ex- 
tremely intricate, requiring for its solution, a skilful and 
laborious application of the most refined analysis. This 
difficulty arises from several circumstances peculiar to 
comets. In the first place, from the elongated form of 
the orbits which these bodies describe, it is during only 
a very small portion of their course that they are visible 
from the earth, and the observations made in that short 
period cannot afterwards be verified on more convenient 
occasions ; whereas in the case of the planets, whose or- 
bits are nearly circular, and whose movements may be 
followed uninterruptedly throughout a complete revolu- 
tion, no such impediments to the determination of their 
orbits occur. In the second place, there are many com- 
ets which move in a direction opposite to the order of 
the signs in the zodiac, and sometimes nearly perpen- 
dicular to the plane of the ecliptic ; so that their appa- 
rent course through the heavens is rendered extremely 
complicated, on account of the contrary motion of the 
earth. In the third place, as there may be a multitude 
of elliptic orbits, whose perihelion distances are equal 
(see p. 100), it is obvious that, in the case of very eccen- 
tric orbits, the slightest change in the position of the 
curve near the vertex, where alone the comet can be ob- 



287. How do the orbits of comets differ from those of planets ? 



ORBITS AND MOTIONS OF COMETS. 231 

served, must occasion a very sensible difference in the 
length of the orbit ; and therefore, though a small error 
produces no perceptible discrepancy between the ob- 
served and the calculated course, while the comet re- 
mains visible from the earth, its effect, when diffused 
over the whole extent of the orbit, may acquire a most 
material or even a fatal importance. 

289. On account of these circumstances, it is found 
exceedingly difficult to lay down the path which a comet 
actually follows through the whole system, and least of 
all, possible to ascertain with accuracy the length of 
the major axis of the ellipse, and consequently the peri- 
odical revolution.* An error of only a few seconds may 
cause a difference of many hundred years. In this 
manner, though Bessel determined the revolution of the 
comet of 1769 to be 2089 years, it was found that an 
error of no more than 5" in observation, would alter the 
period either to 2678 years, or to 1692. Some astrono- 
mers, in calculating the orbit of the great comet of 1680, 
have found the length of its greater axis 426 times the 
earth's distance from the sun, and consequently its pe- 
riod 8792 years ; whilst others estimate the greater axis 
430 times the earth's distance, which alters the period 
to 8916 years. JSTewton and Halley, however, judged 
that this comet accomplished its revolution in only 
570 years. 



288. What particulars are called the elements of a comet? 
What is said of the difficulty of determining these elements ? 
Specify the several reasons of this difficulty. 

289. Is it easy to ascertain the major axis of a comet's orbit, 
and its periodic time ? What difference would an error of a few 
seconds occasion? Give examples of this. 



* For when we know the length of the major axis, we can find the 
periodic time by Kepler's law, which applies as well to comets as to 
planets. 



232 



COMETS. 



290. The appearances of the same comet at different 
periods of its return are so various, that we can never 
pronounce a given comet to be the same with one that 
has appeared before, from any peculiarities in its phy- 
sical aspect. The identity of a comet with one already 
on record, is determined by the identity of the elements. 
It was by this means that H alley first established the 
identity of the comet which bears his name, with one 
that had appeared at several preceding ages of the world, 
of which so many particulars were left on record, as to 
enable him to calculate the elements at each period. 
These were as in the following table. 



Time of appear. 
1456 


Inclin. of the orbit. Lon. of Node. 


Lon. of Per. 


Per. Dist. 


Course. 


17° 56' 


48° 30' 


301° 00' 


0.58 


Eetrograde 


1531 


17 56 


49 25 


301 38 


0.57 


" 


1607 


17 02 


50 21 


302 16 


0.58 




1682 


17 42 


50 48 


301 36 


0.58 





On comparing these elements, no doubt could be en- 
tertained that they belonged to one and the same body ; 
and since the interval between the successive returns 
was seen to be 75 or 76 years, Halley ventured to pre- 
dict that it would again return in 1758. Accordingly, 
the astronomers who lived at that period, looked for its 
return with the greatest interest. It was found, how- 
ever, that on its way towards the sun it would pass very 
near to Jupiter and Saturn, and by their action on it, it 
would be retarded for a long time. Clairaut, a distin- 
guished French mathematician, undertook the laborious 
task of estimating the exact amount of this retardation, 
and found it to be no less than 618 days, namely, 100 
days by the action of Jupiter, and 518 days by that of 
Saturn. This would delay its appearance until early in 



290. Can we identify a comet with one that has been seen 
before, by its appearance? How is this identity determined? 
How was Halley's comet proved to be the same with one that 
had appeared before? How was its return predicted? What 
causes alter the periods of its return ? 



ORBITS AND MOTIONS OF COMETS. 233 

the year 1759, and Clairaut fixed its arrival at the peri- 
helion within a month of April 13th. It came to the 
perihelion on the 12th of March. 

291. The return of Halley's comet in 1835, was looked 
for with no less interest than in 1759. Several of the 
most accurate mathematicians of that age had calculated 
its elements with inconceivable labor. Their zeal was 
rewarded by the appearance of the expected visitant at 
the time and place assigned : it travelled the northern 
sky, presenting the very appearances, in most respects, 
that had been^anticipated ; and came to its perihelion 
on the 16th of November, within two clays of the time 
predicted by Pontecoulant, a French mathematician 
who had, it appeared, made the most successful calcu- 
lation.* On its previous return, it was deemed an ex- 
traordinary achievement to have brought the prediction 
within a month of the actual time. 

Many circumstances conspired to render this return 
of Halley's comet an astronomical event of transcendent 
interest. Of all the celestial bodies, its history was the 
most remarkable ; it afforded most triumphant evidence 
of the truth of the doctrine of universal gravitation, and 
of course of the received laws of astronomy ; and it in- 
spired new confidence in the power of that instrument 
(the Calculus) by means of which its elements had been 
investigated. 

292. Encke's comet, by its frequent returns (once in 
3J years), affords peculiar facilities for ascertaining the 
laws of its revolution ; and it has kept the appointments 



291. How was the return of Halley's comet in 1835 regarded 
by astronomers ? What circumstances conspired to produce this 
feeling ? 



* See Professor Looinis's Observations on Hallev's Comet. Amer. 
Jour. Science, 30, 209. 

20* 



234 COMETS. 

made for it with great exactness. On its return in 
1839 it exhibited to the telescope a globular mass of 
nebulous matter, resembling fog, and moved towards 
its perihelion with great rapidity. 

But what has made Encke's comet particularly fa- 
mous, is its having first revealed to us the existence of a 
Resisting Medium in the planetary spaces. It has long 
been a question, whether the earth and planets revolve 
in a perfect void, or whether a fluid of extreme rarity 
may not be diffused through space. A perfect vacuum 
was deemed most probable, because no such effects on 
the motions of the planets could be detected as indicated 
that they encountered a resisting medium. But a feather 
or a lock of cotton propelled with great velocity, might 
render obvious the resistance of a medium which would 
not be perceptible in the motions of a cannon ball. Ac- 
cordingly, Encke's comet is thought to have plainly suf- 
fered a retardation from encountering a resisting medium 
in the planetary regions. The effect of this resistance, 
from the first discovery of the comet to the present time, 
has been to diminish the time of its revolution about 
two days. Such a resistance, by destroying a part of the 
projectile force, would cause the comet to approach 
nearer to the sun, and thus to have its periodic time 
shortened. The ultimate effect of this cause will be to 
bring the comet nearer to the sun at every revolution, 
until it finally falls into that luminary, although many 
thousand years will be required to produce this catas- 
trophe. It is conceivable, indeed, that the effects of 
such a resistance may be counteracted by the attraction 
of one or more of the planets, near which it may pass 
in its successive returns to the sun. 

It is peculiarly interesting to see a portion of matter, 
of a tenuity exceeding the thinnest fog, pursuing its 
path in space, in obedience to the same laws as those 
which regulate such large and heavy bodies as Jupiter 
or Saturn. In a perfect void, a speck of fog, if propelled 
by a suitable projectile force, would revolve around the 
sun, and hold on its way through the widest orbit, with 



ORBITS AND MOTIONS OF COMETS. 235 

as sure and steady a pace as the heaviest and largest 
bodies in the system. 

293. The most remarkable comet of the present cen- 
tury hitherto observed, was the great comet of 1843. 

Fig. 49. 




On the 28th of February of that year, the attention of 
numerous observers, in various parts of the world, was 
arrested by a comet seen in the broad light of day, a 
little eastward of the sun. The comet resembled a white 
cloud of great density, being nearly equally shining 
throughout, with a nucleus as bright as the full moon at 
midnight in a clear sky. During the first week in March, 
the appearance of this body, as seen in the torrid zone, 
was splendid and magnificent, enhanced in both re- 
spects by the transparency of a tropical sky, and the 
higher angle of elevation above that at which it was 



292. Are trie elements of Encke's comet calculated with ex- 
actness '? What was its appearance in 1839 ? What has made 
it peculiarly famous ? Why should it be so favorable for detect- 
ing a resisting medium \ What has been its effect on the mo- 
tions of the comet ? What will be its ultimate effect ? Does the 
extreme tenuity of this body prevent its moving in obedience to 
the laws that regulate the motions of the largest bodies in the 
system ? 



236 COMETS. 

seen by northern observers. As seen at New Haven, 
on the evening of the 17th of March, soon after sunset, 
it extended along the southern sky, below the feet of 
Orion, reaching nearly to the bright star Sirins, being 
about 40° in length, although in the tropical regions its 
apparent length, at the maximum, w r as nearly 70°. It 
was curved a little like a goose-quill, and colored with 
a slight tinge of rose-red, which in a few evenings dis- 
appeared and left it nearly a pearly white. Although 
astronomers have differed in their decisions respecting 
its periodic time, yet it is generally believed to be 
175 years. Of all the comets on record this approached 
nearest to the sun. It almost grazed his luminous sur- 
face, which it swept round with a velocity, at the point 
of nearest approach, of more than one and a quarter 
million of miles per hour, — a velocity sufficient to carry 
it half round the sun in two hours ; while it required 
175 years to complete the other half, through a journey 
extending to the distance from that luminary of more 
than 6000 millions of miles. The heat of the sun when 
the comet was passing its perihelion, was 47,000 greater 
than what falls on the earth. 

294. Of the physical nature of comets, little is under- 
stood. It is usual to account for the variations which 
their tails undergo, by referring them to the agencies of 
heat and cold. The intense heat to which they are 
subject in approaching so near the sun as some of them 
do, is alleged as a sufficient reason for the great expan- 
sion of thin nebulous atmospheres forming their tails ; 
and the inconceivable cold to which they are subject in 
receding to such a distance from the sun, is supposed to 
account for the condensation of the same matter until it 
returns to its original dimensions. Thus the great comet 
of 1680, at its perihelion, approached 166 times nearer 
the sun than the earth, being only 130,000 miles from 



293. Give an account of the great comet of 1843. 



ORBITS AND MOTIONS OF COMETS. 237 

the surface of the sun. The heat which, it must have 
received, was estimated to be equal to 28,000 times that 
which the earth receives in the same time, and 2000 
times hotter than red-hot iron. This temperature would 
be sufficient to volatilize the most obdurate substances, 
and to expand the vapor to vast dimensions ; and the 
opposite effects of the extreme cold to which it would 
be subject in the regions remote from the sun, would be 
adequate to condense it into its former volume. 

This explanation, however, does not account for the 
direction of the tail, extending, as it usually does, only 
in a line opposite to the sun. Some writers therefore, as 
Delambre, suppose that the nebulous matter of the comet, 
after being expanded to such a volume that the par- 
ticles are no longer attracted to the nucleus unless by 
the slightest conceivable force, are carried off in a direc- 
tion from the sun by the impulse of the solar rays them- 
selves. But to assign such a power of communicating 
motion to the sun's rays while they have never been 
proved to have any momentum, is unphilosophical ; and 
we are compelled to place the phenomena of comets' 
tails among the points of astronomy yet to be explained. 

295. Since those comets which have their perihelion 
very near the sun, like the comet of 1680, cross the or- 
bits of all the planets, the possibility that one of them 
may strike the earth, has frequently been suggested. 
Still, it may quiet our apprehensions on this subject, to 
reflect on the vast extent of the planetary spaces, in 
which these bodies are not crowded together as we see 
them erroneously represented in orreries and diagrams, 
but are sparsely scattered at immense distances from 



294. Is the physical nature of comets well understood? How 
are the variations in the lengths of their tails accounted for? 
How near did the comet of 1680 approach to the sun? What 
heat did it acquire ? Does this account for the direction of the 
tail \ How is that accounted for bv some writers ? 



238 METEORIC SHOWERS. 

each other. They are like insects flying in the expanse 
of heaven. If a comet's tail lay with its axis in the 
plane of the ecliptic when it was near the sun, we can 
imagine that the tail might sweep over the earth ; but 
the tail may be situated at any angle with the ecliptic 
as well as in the same plane with it, and the chances 
that it will not be in the same plane are almost infinite. 
It is also extremely improbable that a comet w T ill cross 
the plane of the ecliptic precisely at the earth's path in 
that plane, since it may as probably cross it at any other 
point, nearer or more remote from the sun. Still, some 
comets have occasionally approached near to the earth. 
Thus Biela's comet, in returning to the sun in 1832, 
crossed the ecliptic very near to the earth's track, and 
had the earth been then at that point of its orbit, it 
might have passed through a portion of the nebulous 
atmosphere of the comet. The earth was within a 
month of reaching that point. This might at first view 
seem to involve some hazard ; yet we must consider that 
a month short, imolied a distance of nearly 50,000,000 
miles. 

METEORIC SHOWERS. 

296. The remarkable exhibitions of shooting stars 
which have occurred within a few years past, have ex- 
cited great interest among astronomers. Their atten- 
tion was first turned towards the subject by the great 
meteoric shower of November 13th, 1833. On that 
morning, from 2 o'clock until broad daylight, the sky 
being perfectly serene and cloudless, the whole heavens 



295. What is said respecting the possibility of a comet's stri- 
king the earth ? What considerations may quiet our apprehen- 
sions ? How might the case be if the tail Jay in the plane of 
the ecliptic ? Is it probable that a comet will cross the ecliptic 
precisely at the place of the earth's path ? Have comets actually 
approached near to the earth ? 



METEORIC SHOWERS. 239 

were lighted up with a magnificent display of celestial 
fireworks. At times the air was filled with streaks of 
light, occasioned by fiery particles darting down so 
swiftly as to leave their impression of light on the eye 
(like a match ignited and whirled before the face), and 
drifting to the northwest like flakes of snow driven by 
the wind ; while, at short intervals, balls of fire, vary- 
ing in size from minute points to bodies as large as Ju- 
piter or Yenus, and in a few instances as large as the 
full moon, descended more slowly along the arch of the 
sky, often leaving after them long trains of light, which 
were in some cases variegated with different prismatic 
colore. On tracing back the lines of direction in which 
the meteors moved, it was found that they all appeared 
to radiate from the same point, wmich was situated near 
one of the stars of the constellation Leo, named Gamma 
Leonis / and in every repetition of the meteoric shower 
of November, the meteors have appeared to radiate 
frorn nearly the same place. 

297. This shower pervaded nearly the whole of North 
America, having appeared in almost equal splendor from 
the British possessions on the north, to the West India 
islands and Mexico on the south. Throughout this im- 
mense region, the duration w r as nearly the same. The 
meteors began to attract attention by their unusual fre- 
quency and brilliancy from nine to tvjelve o'clock in the 
evening ; w T ere most striking in their appearance from 
two to four ; arrived at their maximum, in many places, 
about four o'clock • and continued until rendered invisi- 
ble bv the light of clay. 



296. What first turned the attention of astronomers to the 
subject of shooting stars? Describe the meteoric shower of 
November 13th, 1833. From what point among the stars did 
the meteors appear to come ? 

297. Over what countries did this shower prevail ? At what 
time of night did the display commence ? At what hour was it 
greatest ? 



240 METEORIC SHOWERS. 

298. Soon after this occurrence, it was ascertained 
that a similar meteoric shower had appeared in 1799, 
and, what was remarkable, almost exactly at the same 
time of the year, namely, on the morning of the 12th of 
November ; and it soon appeared by accounts received 
from different parts of the world, that this phenomenon 
had occurred on the same 13th of November, in 1830, 
1831, and 1832. Hence, this was evidently independent 
of the casual changes of the atmosphere ; for, having a 
periodical return, it was undoubtedly to be referred to 
astronomical causes, and its recurrence at a certain de- 
finite period of the year, plainly indicated some relation 
to the revolution of the earth around the sun. The fol- 
lowing conclusions respecting the meteoric shower of 
November are believed to be well established, and 
most of them (which were first suggested by the author 
of this work*) are now generally admitted by astron- 
omers, though we cannot here exhibit the evidence on 
which they are founded. It is considered then as esta- 
blished, that the periodical meteors of November have 
their origin beyond the atmosphere, descending to us 
from some body (which from the known constitution of 
the meteors may be called a nebulous body) with which 
the earth falls in, near or through the borders of which 
it passes ; that this body has an independent existence 
as a member of the solar system, its periodic time being 
either a year or half a year, so that for a number of years 
in succession the two bodies meet near the same part of 
the earth's orbit. It is further established, that the me- 
teors consist of light combustible matter ; that they move 
with great velocities, amounting in some instances to a 



298. On what previous years did similar meteoric showers 
appear ? What was the origin of the meteors ? From what kind 
of body did they proceed ? What sort of bodies were the me- 
teors ? With what velocity did they move ? How were they 



* See American Journal of Science. Vols. xxy. and xxvi. 



METEORIC SHOWERS. 241 

velocity not less than that of the earth in its orbit, or 
19 miles per second, or 68,000 miles per hour; that 
some of them are bodies of large size, sometimes nearly 
or quite a mile in diameter ; that when they enter the 
atmosphere, they rapidly and powerfully condense the 
air before them, and thus elicit the heat which sets them 
on fire, as a spark is elicited in an air-match, by being 
suddenly condensed by means of a piston and cylinder ; 
and that they are burned up at a considerable height 
above the earth, sometimes not less than 30 miles. On 
inquiring further into the relations which this " nebu- 
lous body" sustains to the solar system, it was inferred 
to be, like comets, a regular member of the system, re- 
volving around the sun like them, but between the earth 
and the sun ; and there are many reasons for believing 
that it is identical with the nebulous body long known 
under the name of the Zodiacal Light, and that it is in 
fact from the outer extremities of this singular Light 
that the meteors are derived, being attracted down to 
the earth at that point where the earth in its annual re- 
volution approaches nearest, or perhaps passes through 
the extremities of the Zodiacal Light.* 



set on fire ? What relations did this nebulous body sustain to the 
solar system? With what known body is it supposed to be 
identified ? 

* See a paper on this subject by the author of the present work, in 
the Transactions of the American Association for the Advancement of 
Science, for 1851 ; or American Journal of Science for November, 1851. 

21 



l»ABT III.— OF THE FIXED STARS. 



CHAPTER I. 



OF TEE CONSTELLATIONS. 



299. Tee Fixed Stars are so called, because, to com- 
mon observation, they always maintain the same situa- 
tions with respect to one another. 

The stars are classed by their apparent magnitudes. 
The whole number of magnitudes recorded are sixteen, 
of which the first six only are visible to the naked eye ; 
the rest are telescopic stars. As the stars which are 
now grouped together under one of the first six magni- 
tudes are very unequal among themselves, it has recently 
been proposed to subdivide each class into three, making 
in all eighteen instead of six magnitudes visible to the 
naked eye. These magnitudes are not determined by 
any very definite scale, but are merely ranked according 
to their relative degrees of brightness, and this is left in 
a great measure to the decision of the eye alone, al- 
though it would appear easy to measure the compara- 
tive degree of light in a star by a photometer, and upon 
such measurement to ground a more scientific classifica- 
tion of the stars. The brightest stars, to the number of 
15 or 20, are considered as stars of the first magnitude ; 
the 50 or 60 next brightest, of the second magnitude ; 



299. Why are the fixed stars so called? How are they 
classed? What is*tke whole number of magnitudes ? How 
many of these are visible to the naked eye ? How many of the 
first, second, and the third magnitude respectively ? 



CONSTELLATIONS. 243 

the next 200 of the third magnitude ; and thus the num- 
ber of each class increases rapidly as we descend the 
scale, so that no less than fifteen or twenty thousand are 
included within the first seven magnitudes. 

300. The stars have been grouped in Constellations 
from the most remote antiquity : a few, as Orion, Bootes, 
and Ursa Major, are mentioned in the most ancient 
writings under the same names as they bear at present. 
The names of the constellations are sometimes founded 
on a supposed resemblance to the objects to which the 
names belong ; as the Swan and the Scorpion were 
evidently so denominated from their likeness to those 
animals ; but in most cases it is impossible for us to 
find any reason for designating a constellation by the 
figure of the animal or the hero which is employed to 
represent it. These representations were probably once 
blended with the fables of pagan mythology. The 
same figures, absurd as they appear, are still retained 
for the convenience of reference ; since it is easy to 
find any particular star, by specifying the part of the 
figure to which it belongs, as when we say a star is in 
the neck of Taurus, in the knee of Hercules, or in the 
tail of the Great Bear. This method furnishes a general 
clue to its position ; but the stars belonging to any con- 
stellation are distinguished according to their apparent 
magnitudes, as follows : — first, by the Greek letters, 
Alpha, Beta, Gamma, &c. Thus Alpha Orionis, de- 
notes the largest star in Orion, Beta A.?idromedce, the 
second star in Andromeda, and Gamma Leonis, the 
third brightest star in the Lion. Where the number of 
the Greek letters is insufficient to include all the stars 
in a constellation, recourse is had to the letters of the 
Roman alphabet, a, b, c, &c. ; and, in cases where 



300. What constellations have been known from antiquity? 
Why are the ancient names preserved ? How are the individual 
stars of a constellation named ? 



244 CONSTELLATIONS. 

these are exhausted, the final resort is to numbers. 
This is evidently necessary, since the largest constel- 
lations contain many hundreds or even thousands of 
stars. 

301. The earliest catalogue of the stars was made by 
ITipparchus, of the Alexandrian School, about 140 
years before the Christian era. A new star appearing 
in the firmament, he was induced to count the stars and 
to record their positions, in order that posterity might 
be able to judge of the permanency of the constella- 
tions. His catalogue contains all that were conspicuous 
to the naked eye in the latitude of Alexandria, being 
1022. Most persons unacquainted with the actual num- 
ber of the stars which compose the visible firmament, 
would suppose it to be much greater than this ; but it 
is found that the catalogue of Hipparchus embraces 
nearly all that can now be seen in the same latitude, 
and that on the equator, where the spectator has the 
northern and southern hemispheres both in view, the 
number of stars that can be counted does not exceed 
3000. A careless view of the firmament in a clear 
night, gives us the impression of an infinite multitude 
of stars ; but when we begin to count them, they ap- 
pear much more sparsely distributed than we supposed, 
and large portions of the sky appear almost destitute 
of stars. 

By the aid of the telescope, new fields of stars pre- 
sent themselves of boundless extent ; the number con- 
tinually augmenting as the powers of the telescope are 
increased. Lalancle, in his Histoire Celeste, has re- 
gistered the positions of no less than 50,000 ; and the 
whole number visible in the largest telescopes amount 
to many millions. 



301. "Who made the earliest catalogue of stars ? How many 
did it contain ? How many can be seen with the naked eye ? 
flow many by the telescope ? 



CONSTELLATIONS. 245 

302. It is strongly recommended to the learner to 
acquaint himself with the leading constellations at 
least, and with a few of the most remarkable individual 
stars. The task of learning them is comparatively easy, 
when they are taken up at suitable intervals throughout 
the year, the moon being absent and the sky clear. 
After becoming familiar with such constellations as are 
visible on any given evening (suppose the first of Jan- 
uary), these may be carefully reviewed after an interval 
of a month, and the several new ones added which have 
in the mean time risen above the eastern horizon. By 
repeating this process near the beginning of every 
month of the year, the learner will acquire a competent 
knowledge of the whole that are visible in his latitude, 
and with a small expenditure of time. It may at first 
be advisable to obtain, for an evening or two, the assist- 
ance of some one who is acquainted with the constel- 
lations, to point out such as are then visible in .the 
evening sky. Then, by the aid of a celestial map, or, 
what is better, a celestial globe, the learner will pursue 
the study without difficulty. We begin by rectifying 
the globe for the time, according to the directions given 
in Article 61. 

In the following sketch of the leading constellations, 
we will point out a few of the marks by which they 
may be severally recognized, adding occasionally a few 
particulars, and leaving it to the learner to fill up the 
outline by the aid of his map or globe, one of which, 
indeed, is presumed to be before him.* But, by way 
of giving a lead, we will indicate by diagrams the rel- 
ative positions of a few of the principal stars of the 
most conspicuous constellations, especially of such as 
have remarkable figures. Our diagrams, being neces- 
sarily small, do not represent the relative sizes of the 



* A celestial globe, sufficient for studying the constellations, may be 
purchased for a small sum, and is, in other respects, a valuable posses- 
don to the astronomical student ; but even cheap maps of the stars, 
like those of Burritt or Kendal, "will answer for beginners; and the 

21* 



246 CONSTELLATIONS. 

constellations. Those may be learned from globes or 
maps. 

Let ns begin with the constellations of the Zodiac, 
which, succeeding each other as they do in a known 
order, are most easily found * AEmg 

Aries (The Ram) the first constella- ^ 
tion of the Zodiac, is known by two d^ n^, 

bright stars, Alpha on the northeast, p 

and Beta on the southwest, 4°f apart, ^ 

forming the head. South of Beta, at 
the distance of 2°, is a smaller star, Gamma. The 
next brightest star of the Earn, Delta, is in the tail, 15° 
southeast of Alpha. The feet of the figure rest on the 
head of the Whale. 

Taurus (The Bull) will be readily found by the seven 
stars, or Pleiades, which lie in the neck, 24° eastward 
of Arietis. The largest star in Taurus is Aldebaran, 
of the first magnitude, in the Bull's eye, 10° southeast 
of the Pleiades. It has a reddish color, and resembles 
the planet Mars. The other eye of the figure is Epsi- 
lon, 3° northwest of Aldebaran. Five small stars, 



Celestial Atlas, published by the Society for the Diffusion of Useful 
Knowledge, which is suitable for the more advanced student, may be 
procured at a moderate expense. Those who have not studied Greek 
may easily learn the characters denoting the Greek letters. 

* It will be expedient, where it is practicable, for the learner to 
study the constellations in separate portions, at different seasons of the 
year, as at the equinoxes and at the solstices, according to the direc- 
tions given in the closing article of this chapter. A3 the astronomer is 
supposed to face the south, the right side becomes west, and the left 
side east. 

\ These measures are not intended to be stated with minute accu- 
racy, but only with such a degree of exactness as may serve for a 
general guide. The learner will find it greatly for his advantage to 
accustom himself to make an accurate estimate with the eye of dis- 
tances in degrees on the celestial sphere ; and he may, at the outset, 
fix on the distance between Alpha and Beta Arietis as a standard 
measure (4°) by which to estimate other angular distances among the 
stars. Thus, half this length applied from Beta to Gamma, indicates 
that the two latter stars are 2° apart ; and two and a half times the 
same measure (10°) will reach from the Pleiades to Aldebaran. Or the 
Pointers in the Great Bear will furnish a measure of 5°. 



CONSTELLATIOXS. 247 

situated a little west of Aldebaran, in the face of the 
Bull, constitute the Hyades. Although the Pleiades 

Taurus. Pleiades. 



are usually denominated the seven stars, yet it has 
been remarked, from a high antiquity, that only six are 
present.* 

Some persons, however, of remarkable powers of 
vision, are still able to recognize seven, and even a 
greater number, f With a moderate telescope, not less 
than 50 or 60 stars, of considerable brightness, may be 
counted in this group, and a much larger number of 
very small stars are revealed to the more powerful 
telescopes. The beautiful allusion, in the Book of Job, 
to the " sweet influences of the Pleiades," and the 
special mention made of this group by Homer and 
Hesiod, show how early it had attracted the attention of 
mankind. The horns of the Bull are two stars, Beta 
and Zeta, situated 25° east of the Pleiades, being 8° 
apart. The northern horn, Beta, also forms one of the 
feet of Auriga, the Charioteer. 

Gemini (The Twins) is represented by two well-known 
stars, Castor and Pollux, in the head of the figure, 5° 
asunder. Castor, the northern, is of the first, and 
Pollux of the second magnitude. Four conspicuous 
stars, extending in a line from south to north, 25° S. "W. 
of Castor, form the feet, and two others parallel to these, 



* Their names were Eleetra, Maia, Taygeta, Alcyone, Celseno, As- 
terope, and Merope, the last being the " Lost Pleiad" of the poets. 
Alcyone, according to a recent celebrated hypothesis, is distinguished 
as the center around which the starry host revolve. 

f Smyth's Cycle, II. 86. 



248 CONSTELLATIONS. 

at the distance of six or seven degrees ^ E Twl!?s - 

northeastward, are in the knees. p ^ 

Cancer (The Crab). There are no * 
large stars in this constellation, and 
it is regarded as less remarkable than 
any other in the Zodiac. The two 
most conspicuous stars, Alpha and 
Beta, are in the southern claws of 6 ^ 

the figure; and in its body are the * 
northern and southern Asellus, which 
may be readily found on a celestial ^ * 

globe. But the most remarkable 7& 

object in this constellation, is a misty 
group of very small stars, so close together when seen 
by the naked eye as to resemble a comet, but easily 
separated by the telescope into a beautiful collection 'of 
brilliant points. It is called Prcesepe, or the Beehive. 

Leo (The Lion) is a very large constellation, and has 
many interesting members. Megulus (a Leonis) is a star 



The Liox, 

ft 



p ^ - 

; % 

of the first magnitude, which lies very near the ecliptic, 
and is much used in astronomical observations. North 
of Regulus lies a semicircle of five bright stars, arranged 
in the form of a sickle, of which Regulus is the handle, 
and extending over the shoulder and neck of the Lion.* 

* As the Meteors of November always appear to radiate from a point 
in the bend of the sickle, near the star Gamma, it may be noted that 
the names of the six stars composing this figure, beginning with Kegu- 
ius, are a, v, y, I, p, *• 



CONSTELLATIONS. 249 

Denebola, a conspicuous star in the Lion's tail, lies 25° 
east of Kegulus. Twenty bright stars in all help to 
compose this beautiful constellation. It ranges from 
west to east along the Zodiac, over more than 40° of 
longitude, all parts of the figure excepting the feet lying 
north of the ecliptic. 

Virgo (The Virgin) extends along the Zodiac east- 
ward from the Lion, covering an equally wide region 
of the heavens, although less distinguished by brilliant 
stars. Spica, however, is a star of the first magnitude, 
and lies a little east of the vernal equinox. Vindemi- 
atrix, in the arm of Virgo, 18° east of Denebola, and 
23° north of Spica, is easily found ; and directly south 
of Denebola 13°, is Beta Virginis ; while four other-con- 
spicuous stars, in the form of a trapezium, between this 
and Vindemiatrix, lie in the wing and shoulders of the 
figure. The feet are near the Balance. 

Libra (The Balance) is composed of a few scattered 
members situated between the feet of Virgo and the 
head of Scorpio, but has no very distinctive marks. 
Two stars of the second magnitude, Alpha on the south, 
and Beta 8° northeast of Alpha, together with a few 
smaller stars, form the scales. 

Scorpio (The Scorpion) is one of the finest of the con- 
stellations of the Zodiac, and is manifestly so called 
from its resemblance to the animal whose name it bears. 
The head is composed of five stars, arranged in a line 
slightly curved, which is crossed in the center by the eclip- 
tic, nearly at right angles, a degree south of the bright- 
est of the group Beta Scorpionis. Nine degrees south- 
east of this is a remarkable star of the first magnitude, 
called Antares, and sometimes the Seccrt of the Scor- 
pion. It is of a red color, resembling the planet Mars. 
ISouth and east of this, a succession of not less than 
nine bright stars sweep round in a semicircle, termina- 
ting in several small stars forming the sting of the Scor- 
pion. The tail of the figure extends into the Milky 
Way. 



250 CONSTELLATIONS. 

Thb Scorpion. 



»* 






* 



* 



%V 



Sagittarius (The Archer). Ten degrees eastward 
of the Scorpion's tail, on the eastern margin of the 
Milky Way, we come to the bow of Sagittarius, con- 
sisting of three stars about 6° apart, the middle one 
being the brightest, and situated in the bend of the bow, 
while a fourth star, 4° westward of it, constitutes the 
arrow. The archer is represented by the figure of a 
Centaur (half horse and half man), and proceeding 
about ten degrees east from the bow, we come to a 
collection of seven or eight stars of the second and third 
magnitudes, which lie in the human or upper part of 
the figure. 

Capricornus (The Goat), represented with the head 
of a goat and the tail of a fish, comes next to Sagitta- 
rius, about 20° eastward of the group that form the 
upper portions of that constellation. Two stars of the 
second magnitude, Alpha on the north, and Beta on 
the south, 3° apart, constitute the head of Capricornus, 
while a collection of stars of the third magnitude, lying 
20° southeast of these, form the tail. 

Aquarius (The Water Bearer) is closely in contact 
with the tail of Capricornus, immediately north of 
which, at the distance of 10°, is the western shoulder 



CONSTELLATIONS. 251 

(Beta), and 10° further east is the eastern shoulder, 
(Alpha) of Aquarius. About 3° southeast of Alpha is 
Gamma Aquarii, which, together with the other two, 
makes an acute triangle, of which Beta forms the ver- 
tex. In the eastern arm of Aquarius are found four 
stars, which together make the figure Y, the open part 
being westward, or towards the shoulders of the con- 
stellation. Aquarius ranges nearly 30° from north to 
south, being nearly bisected by the ecliptic. 

Pisces (The Fishes). Three figures of this kind, at a 
great distance apart, two north and one south of the 
ecliptic, compose this constellation. The southern Fish, 
Piscis Australia, otherwise called Pomalhaut, lies 
directly below the feet of Aquarius, and being the only 
conspicuous star in that part of the heavens, is much 
used in astronomical measurements. It is 30° south of 
the equator. 

About 12° east of the figure Y in the arm of Aqua- 
rius, is an assemblage of five stars, forming a pretty 
regular pentagon, which is one of the northern mem- 
bers of the Constellation Pisces ; and far to the north- 
east of this figure, north of the head of Aries, lies the 
third member, the three being represented as connected 
together by a ribbon, or wavy band, composed of minute 
stars. 

303. The Constellations of the Zodiac, being first well 
learned, so as to be readily recognized, will facilitate 
the learning of others that lie north and south of them. 
Let us therefore next review the principal Northern 
Constellations, beginning at the North Pole. 

Ursa Minor (The Little Bear). The Pole-star 
(Polaris) is in the extremity of the tail of the Little 
Bear. It is of the third magnitude, and being within 



302. What directions are given for learning the constellations ? 
Describe successively the constellations Aries, Taurus, Gemini, 
Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, 
Aquarius, Pisces. 



252 CONSTELLATIONS. 

less than a degree and a half of the North. Pole of the 
heavens, it serves at present to indicate the position of 

The Little Beab. 

''''>Yf 



7#' * *.. 



/?* 






# 



the pole. It will be recollected, however, that on ac- 
count of the precession of the equinoxes, the pole of 
the heavens is constantly shifting its place from east to 
west, revolving about the pole of the ecliptic, and will 
in time recede so far from the pole-star, that this will 
no longer retain its present distinction (Art. 138). Three 
stars in a straight line, 4° or 5° apart, commencing with 
Polaris, lead to a trapezium of four stars, the whole 
seven together forming the figure of a dipper, the tra- 
pezium being the body, and the three first-mentioned 
stars being the handle. 

Ursa Major (The Great Bear) is one of the largest 
and most celebrated of the constellations. It is usuallv 



The Ore at Bea.e. 



P 



recognized by the figure of a larger and more perfect 
dipper than the one in the Little Bear — three stars, as 
before, constituting the handle, and four others, in the 
form of a trapezium, the body of the figure. The two 
western stars of the trapezium, ranging nearly with the 
North Star, are called the Pointers ; and beginning 



■M 



CONSTELLATIONS. 253 

with the northern of these two, and following round from 
left to right through the whole seven, they correspond 
in rank to the succession of the first seven letters of the 
Greek alphabet, Alpha, Beta, Gamma, Delta, Epsilon, 
Zeta, Eta. Several of them also are known by their 
Arabic names. Thus, the first in the tail, corresponding 
to Epsilon, is Aliotli, the next (Zeta) Mizar, and the 
last (Eta) Benetnasch. These are all bright and beauti- 
ful stars, Alpha being of the first magnitude, Beta, 
Gamma, Delta, of the second, and the three forming 
the tail, of the third. But it must be remarked that 
this very remarkable figure of a dipper or ladle com- 
poses but a small part of the entire constellation, being 
merely the hinder half of the body and the tail of the 
Bear. The head and breast of the figure, lying about 
ten or twelve degrees west of the Pointers, contain a 
great number of minute stars in a triangular group. 
One of the fourth magnitude, Omicron, is in the mouth 
of the Bear. The feet of the figure may be looked for 
about 15° south of those already described, the two 
hinder paws consisting each of two stars very similar 
in appearance, and only a degree and a half apart. 
The two paws are distant from each other about 18° ; 
and following westward about the same number of de- 
grees, we come to another very similar pair of stars, which 
constitute one of the fore paws, the other foot being with- 
out any corresponding pair. 

In a clear winter's night, when the whole constella- 
tion is above the pole, these various parts may be easily 
recognized, and the entire figure will be seen to resem- 
ble a large animal, readily accounting for the name 
given to this constellation from the earliest ages. 

Draco (The Dragon) is also a very large constella- 
tion, extending for a great length from east to west. 
Beginning at the tail, which lies half way between the 
Pointers and the Pole-star, and winding round between 
the Great and the Little Bear, by a continued succession 
of bright stars from 5° to 10° asunder, it coils around 
under the feet of the Little Bear, sweeps round the pole 



254 CONSTELLATIONS. 

of the ecliptic, and terminates in a trapezium formed 
by four conspicuous stars, from thirty to thirty-five de- 
grees from the North Pole. A few of the members of 
this constellation are of the second, but the greater part 
of the third magnitude, and below it. 

304. "With the constellations already described as 
general landmarks, we may now proceed with each of 
the principal remaining ones, by stating its boundaries, 
as we do those of countries in geography ; their relative 
situations being thus first learned from a map, or (what 
is better) from a celestial globe, and then being severally 
traced out on the sky itself. We will begin with those 
which surround the North Pole. 

Cepheus (The King) is bounded ~N. by the Little Bear, 
E. by Cassiopeia, S. by the Lizard, and W. by the 
Dragon. The head lies in the Milky Way, and the feet 
extend towards the pole. It contains no stars above the 
third magnitude. 



Cassiopeia. 

i 



""-** 



Cassiopeia is bounded E". and W. by Cepheus, E. by 
Camelopardalus, and S. by Andromeda, and is one of 
the constellations of the Milky Way. It is readily dis- 
tinguished by the figure of a chair inverted, of which 
two stars constitute the back, and four, in the form of a 
square, the body of the chair. It is on the opposite side 
of the pole from the Great Bear, and nearly at the same 
distance from it. 



303. Describe the Northern Constellations, Ursa Minor, Ursa 
Major, Draco. 



CONSTELLATIONS. 255 

Camelopardaltjs (The Giraffe) is bounded N. by the 
Little Bear, E. by the head of the Great Bear, S. by 
Auriga and Perseus, and W. by Cassiopeia. Although 
this constellation occupies a large space, yet it has no 
conspicuous stars. 

Andromeda is bounded 1ST. by Cassiopeia, E. by Per- 
seus, S. by Pegasus, and "W". by the Lizard. The direc- 
tion of the figure is from S. W. to N". E., the head coming 
down within 30° of the equator, and being recognized 
by a star of the second magnitude, which forms the 
northeastern corner of the great square in Pegasus, to 
be described hereafter. At the distance of six or seven 
degrees from the head, are three conspicuous stars in a 
row, ranging from north to south, which lie in the 
breast of the figure ; and about the same distance from 
these, and parallel to them, three more, which consti- 
tute the girdle of Andromeda. Near the northernmost 
of the three, is a faint, misty object, often mistaken for 
a comet, but is a nebula, and one of the most remarka- 
ble in the heavens. 

Perseus is bounded 1ST. by Cassiopeia, E. by Auriga, 
S. by Taurus, and W. by Andromeda. The figure ex- 
tends from north to south, and is represented by a giant 
holding aloft a sword in his right hand, while his left 
grasps the head of Medusa, — a group of stars on the 
western side of the figure, embracing the celebrated 
star Algol. A series of bright stars descend along the 
shoulders and the waist, and there divide into the two 
legs. The western foot is 8° north of the Pleiades. 
The eastern leg is bent at the knee, which is distin- 
guished by a group of small stars. Near the sword 
handle, under Cassiopeia's chair, is a fine cluster of stars, 
so close together as scarcely to be separable by the eye. 

Auriga (The Wagoner) is bounded ~N. by Camelo- 
pardalus, E. by the Lynx, S. by Taurus, and W. by 
Perseus. He is represented as bearing on his left 
shoulder the little Goat Capella, a white and beautiful 
star of the first magnitude, while Beta forms the 
vight shoulder, 8° east of Capella. These two bright 



256 CONSTELLATIONS. 

stars form, with tlie northern horn of the Bull, at the 
distance of 18°, an isosceles triangle. 

Leo Minor (The Lesser Lion) is bounded !N". by Ursa 
Major, E. by Coma Berenices, S. by Leo, and W. by 
the Lynx. It lies directly under the hind feet of the 
Great Bear, and over the sickle in Leo, and is easily 
distinguished. Four stars in the central part of the 
figure, from 4° to 5° apart, form a pretty regular par- 
allelogram. 

Canes Yenatici (The Greyhounds). This constella- 
tion lies between the hind legs of the Great Bear on 
the west, and Bootes on the east ; Cor Caroli, a soli- 
tary star of the third magnitude, 18° south of Alioth, 
in the tail of the Great Bear, will serve to mark this 
constellation. 

Coma Berenices (Berenice's Hair) is a cluster of 
small stars, composing a rich group, 15° !N". E. of Dene- 
bola, in the Lion's tail, in a line between this star and 
Cor Caroli, and half way between the two. 

Bootes is bounded $". by Draco, E. by the Crown 
and the head of Serpentarius, S. by Virgo, and W. by 
Coma Berenices and the Hounds. It reaches for a great 
distance from north to south, the head being within 20° 
of the Dragon, and the feet extending to the Zodiac. In 
the knee of Bootes is Arcturus, a star of the first mag- 
nitude. The next brightest star, Beta, is in the head of 
Bootes, 23° north of Arcturus, and 15° east of the last 
star in the tail of the Great Bear. e ^ thbCrown. 

Corona Borealis (The North- / #.£ 

ern Crown) is bounded 1ST. and ; \ 

E. by Hercules, S. by the head of *# 
Serpentarius, and W. by Bootes. \ %p 

It is formed of a semicircle of "•-"•#—*■"* 

bright stare, six in number, of which Gamma, near the 
center of the curve, is of the second magnitude. 

Hercules is bounded E". by Draco, E. by Lyra, S. 
by Ophiuchus, and W. by Corona Borealis. It is a 
very large constellation, and contains some brilliant 
objects for the telescope, although its components are 



CONSTELLATIONS. 



257 



generally very small. The figure lies north and south, 
with the 'head near the head of Ophiuchus, and the 
feet under the head of Draco. Being between the 
Crown and the Lyre, its locality is easily determined. 
The eastern foot of Hercules forms an isosceles triangle 
with the two southern stars of the trapezium in the head 
of Draco ; while the head of Hercules is far in the 
south, within 15° of the equator, being 6° west of a 
similar star which constitutes the head of Ophiuchus. 

Ltea (The Lyke) is bounded N. by the head of Draco, 
E. by the Swan, S. and W. by Hercules. Alpha Lyrse, 
or Vega, is of the first magnitude. It is accompanied 
by a small acute triangle of stars. Its color is a shining 
white, resembling Capella and the Eagle. 

Cygnus (The Swan) extends along the Milky Way, 
below Cepheus, and immediately eastward of the Lyre, 

The Swan. 

%5 









£* 



and has the figure of a large bird flying along the Milky 
"Way from north to south, with outstretched wings and 
long neck. Commencing with the tail, 25° east of Lyra, 
and following down the Milky Way, we pass along a 
line of conspicuous stars which form the body and neck 
of the figure ; and then returning to the second of the 
series, we see two bright stars at eight or nine degrees 
on the right and left (the three together ranging across 
the Milky Way), which form the wings of the Swan. 
This constellation is among the few which exhibit 
some resemblance to the animals whose names they 
bear. 

22* 



258 CONSTELLATIONS. 

Vulpecula (The Little Fox) is a small constellation, 
in which a fox is represented as holding a goose in 
his mouth. It lies in the Milky "Way, between the 
Swan on the north and the Dolphin and the Arrow on 
the south. 

Aquila (The Eagle) stretches across the Milky "Way, 
and is bounded N. by Sagitta, a small constellation 
which separates it from the Fox, E. by the Dolphin, 
S. by Antinous, and W. by Taurus Poniatowski (the 
Polish Bull), which separates it from Ophiuchus. It is 
distinguished by three bright stars in the neck, known 
as the " three stars," which lie in a straight line about 
2° apart, on the eastern margin of the Milky Way. 
The central star is of the first magnitude. Its Arabic 
name is Altair. 

Antinous lies across the equator, between the Eagle 
on the north, and the head of- Capricorn on the south. 

Delphlnus (The Dolphin) is situated east and north 
of Altair, and is composed of five stars of the third 
magnitude, of which four, in the form of a rhombus, 
compose the head, and the fifth forms the tail. 

Pegasus (The Flying Hoese) is a very large constel- 
lation, and is bounded !N". by the Lizard and Andromeda, 
E. and S. by Pisces, W. by the Dolphin. The head is near 
the Dolphin, while the back rests on Pisces, and the feet 
extend towards Andromeda. 

A large sqiiare, composed of four conspicuous mem- 
bers, one (Markah) of the first, and three others of the 
second magnitude, distinguish this constellation. The 
corners of the square are about 15° apart, the north- 
eastern corner being in the head of Andromeda. 

Ophiuchus is another very large constellation, the 
head being near the head of Hercules, and the feet 



304. Bound and describe the following constellations, Ce- 
pheus, Cassiopeia, Camelopardalus, Andromeda, Perseus, Leo 
Minor, Canes Venatici, Coma Berenices, Bootes, Corona Bore- 
alis, Hercules, Lyra, Cygnus, Vulpecula, Aquila, Antinous, Del- 
phi nus, Pegasus, Ophiuchus. 



CONSTELLATIONS. 259 

reaching to Scorpio, the western foot being almost in 
contact with Antares. The figure is that of a giant 
holding a serpent in his hands. The head of the serpent 
is a little south of the Crown, and the tail reaches far 
eastward towards the Eagle. 

305. Of the constellations which lie south of the 
Zodiac, we shall notice only Cetns, Orion, Lepus, Mon- 
oceros, Canis Major, Canis Minor, Hydra, Crater, and 
Corvus. 

Cetus (The Whale) is distinguished rather for its 
extent than its brillancy, occupying a large tract of the 
sky south of the constellations Pisces and Aries. The 
head is directly below the head of Aries, and the tail 
reaches westward 45°, being about 10° south of the 
vernal equinox. Menkar (a Ceti), the largest of its com- 
ponents, is situated in the mouth, 25° southeast of a Arie- 
tis ; and Mira (o Ceti), in the neck, 14° west of Menkar, 
is celebrated as a variable star, which exhibits different 
magnitudes at different times. 

Oeion is one of the most magnificent of the constel- 
lations, and one of those that have longest attracted the 
admiration of mankind, being alluded, to in the Book 
of Job, and mentioned by Homer. The head of Orion 
lies southeast of Taurus,. 15° from Aldebaran, and is 
composed of a cluster of small stars. Two very bright 
stars, Betelgeuse of the first, and Bellairrix of the second 
magnitude, form the shoulders ; three more, resembling 
the three stars of the Eagle, compose the girdle ; and 
three smaller stars, in a line inclined to the girdle, form 
the sword. Rigel, of the first magnitude, makes the west 
foot, but the corresponding star, 9° southeast of this, 
which is sometimes taken for the other foot, is above 
the knee, this foot being concealed behind the Hare. 
Orion's club is marked by three stars of the fifth mag- 
nitude, close together, in the Milky Way, just below 
the southern horn of the Bull. Orion is a favorite con- 
stellation with the practical astronomer, abounding, as 
it does, in addition to the splendor of its components, 



260 CONSTELLATIONS. 

with fine nebulse, double stars, and other objects of 
peculiar interest when viewed with the telescope. It 

Orion. 



a%. 



*# 



* 



7-& 



m 



embraces 70 stars, plainly visible to the naked eye, in- 
cluding two of the first, four of the second, and three 
of the third magnitude. 

Lepus (The Hare). Below Rigel, the western foot 
of Orion, is a small trapezium of stars, which forms the 
ears of the Hare ; and an assemblage of nine stars, of 
the third and fourth magnitudes, south and east of these, 
make up the remaining parts of the figure. 

Canis Major (The Greater Dog) lies directly east of 
the Hare, and is highly distinguished by containing 
Sirius, the most splendid of all the fixed stars, which 
lies in the mouth of the figure. In the fore paw, 6° 
west of Sirius, is a star of the second magnitude 
((3 Canis Mag oris), and from 10° to 15° south of Sirius, 
is a collection of stars of the second and third magni- 
tudes, which make up the hinder portions of the figure. 
The Egyptians, who anticipated the rising of the Nile 
by the appearance of Sirius in the morning sky, repre- 
sented the constellation by the figure of a dog, the 
symbol of a faithful watchman. 

Canis Minor (The Lesser Dog). About 25° north of 
Sirius, is the bright star Procyon, also of the first mag- 



CONSTELLATIONS. 261 

nitude, which marks the side of the Lesser Dog. A 
star of the third magnitude (/3), 4° northwest of this, in 
the head of the figure, forms with Proeyon the lower 
side of an elongated jDarallelogram, of which Castor and 
Pollux, 25° north, form the upper side. 

Monoceeos is a large constellation, occupying the 
space between the Greater and the Lesser Dog, but has 
no conspicuous members. 

Hydka occupies a long "space south of Leo, Yirgo, 
and Libra. Its head, which is south of the fore paws 
of the Lion, consists of four stars of the fourth magni- 
tude, of nearly uniform appearance ; and about 15° S. 
E. of these is the Heart [Cor Hydrce), 23° south of 
Regulus. Resting on Hydra, and south of the hind 
feet of Leo, is Crater (the Cup), consisting of six stars 
of the fourth magnitude, arranged in the form of a 
semicircle ; and a little further east, also perched on 
the back of Hydra, is Corvus (the Crow), the two 
brightest components of which are situated in one of 
the wings of the figure, in a line between Crater and 
Spica ~\ irginis. 

306. According to an intimation given in a note on 
p. 246, the constellations may be advantageously studied 
at four different periods of the year, as near the equi- 
noxes and the solstices, according to the following direc- 
tions. The latitude supposed is 41°. 

Lesson I. — For the middle of September, from 8 to 
10 o'clock. At 8 o'clock Scorpio is near setting in the 
S. W., Antares being 10° high. The bow of Sagittarius 
is seen on the eastern margin of the Milky Way, the 
arrow being directed to a point a little below Antares. 
At 9 o'clock, the horns of the Goat come upon the 
meridian ; and at 10 o'clock, the western shoulder of 



305. Describe the constellations south of the Zodiac, Cetus, 
Orion, Lepus, Monoceros, Cards Major, Canis Minor, Hydra, 
Crater, Corvus. 



262 CONSTELLATIONS. 

Aquarius. The other shoulder, and the figure Y in the 
arm, may also be easily found from the description 
given on p. 251 ; also, the Pentagon, in Pisces, and 
Fomalhaut (the Southern Fish), a solitary bright star far 
in the south, only 16° above the horizon. The head of 
Aries appears in the east, and the Pleiades are but 
little above the horizon, while Aldebaran is just rising. 
Returning now to the west* (at 10 o'clock), the Crown 
is seen a little north of west, about 20° high ; Lyra is 
30° west of the zenith ; the Swan is nearly overhead : 
and following down the Milky Way, the Eagle is seen 
on its eastern margin over against Lyra on the western ; 
and the Dolphin, a little eastward of the Eagle, and 
as far above the horns of Capricornus as the latter are 
above the southern horizon. Following on the east of 
the meridian, the great square in Pegasus may next be 
identified ; and since the northeastern corner of the 
square is in the head of Andromeda, this constellation 
may next be learned ; and then Perseus and Auriga, 
which appear still further east. Directly north of Per- 
seus, is Cassiopeia's chair ; and next to that we may 
take the Pole-star, the Little Bear, and the Great Bear, 
the Dipper only being traced for the present. Com- 
mencing now at the tail of the Dragon, we may trace 
round this figure between the two Bears to the head, 
which brings us back to Lyra and the feet of Her- 
cules. The boundaries of this constellation, and of 
Ophiuchus, which lies south of it, will end the first 
lesson. 

Lesson II. — For the middle of Decetnber, from 1 to 
10 o'clock. Of the constellations of the Zodiac, 
Taurus and Gemini are now favorably situated for ob- 
servation in the east. At 1 o'clock, the tail of Cetus 
just reaches the meridian, its head being seen below 
the feet of Aries. Orion is just risen in the S. E. At 
9 o'clock, just above the western horizon, are seen in 
succession from south to north, Aquarius, the Dolphin, 
the Eagle, the Lyre, and the Dragon's head. Between 



CONSTELLATIONS. 263 

the Eagle and the Lyre, at a little higher altitude, we 
perceive the Swan, flying directly downwards. Be- 
tween the tail of the Swan and the Pole-star, is Ce- 
pheus ; and from the pole, along the meridian, we trace 
Cassiopeia, the feet of Andromeda, the head of Aries, 
and the neck of the Whale. At 10 o'clock, Perseus 
has reached the meridian, the star Algol, in the head 
of Medusa, being directly overhead. The Pleiades 
are but little eastward of the zenith ; and following 
along south from the pole, at the interval of from one 
to two hours east of the meridian, we may trace in 
succession, Camelopard, Auriga, Taurus, Orion, and 
the Hare. Turning along the eastern horizon, we find 
Canis Major, Monocer-os, Cam's Minor, the head of 
Hydra (just rising), Cancer, Leo, the sickle just ap- 
pearing about 3° north of the east point. Leo Minor 
and Ursa Major complete the survey; and we may now 
advantageously trace out the various parts of the Great 
Bear, as described on p. 252 ; the two stars composing 
its hindmost paw being scarcely above the horizon. 

Lessor III. — For the middle of Mareh, from 8 to 10 
o'clock. At 8 o'clock, we see the Twins nearly over- 
head, and Procyon and Sirius, at different intervals, 
towards the south. Along the west we recognize the 
neck and head of the Whale, the head, of Aries, and 
the head of Andromeda ; next above these, Orion, 
Taurus, Perseus, Cassiopeia, and Cepheus ; and north 
of the head of Orion, we see Auriga and Camelopard. 
In the S., Hydra is now fully displayed ; and fol- 
lowing on north, we obtain fine views of the Greater 
and the Lesser Lion, and the Great Bear. At 9 o'clock, 
Crater and Corvus appear in the S. E. on the back of 
Hydra ; Virgo extends from Leo down to the horizon, 
Spica Virginis being about 5° high ; and north of Vir- 
go, we trace in -succession Coma Berenices, Cor Caroli, 
Bootes, with Arcturus and the Crown lying far in the 
KE. 



264 CONSTELLATIONS. 

Lesson IV. — For the middle of June, from 9 to 10 
o'clock. At 9 o'clock, Bootes, Corona Borealis, the 
head of Libra, the Serpent, and Scorpio, lie along on 
either side of the meridian. Castor and Pollux are just 
setting, and Leo is about an hour high. East of Leo, 
Yirgo is seen extending along towards the meridian, 
Spica being about 30° above the southern horizon. 
North of Leo and Yirgo, we recognize Leo Minor, 
Coma Berenices, Cor Caroli, and Ursa Major. At 10 
o'clock, we trace along the eastern side of the meridian, 
Draco, Hercules, and Ophiuchus ; and east of these, 
the Lyre, the Eagle, Antinous, Sagittarius, and Capri- 
cornus. North of the Eagle, and round to the east, we 
find Cepheus and Cassiopeia, Andromeda rising in the 
northeast, Pegasus in the east, and Aquarius in the 
southeast. Thus we may advantageously complete a 
review of the constellations. 



CHAPTER II. 

DOUBLE STARS— TEMPORARY STARS VARIABLE STARS 

CLUSTERS AND NEBULAE. 

307. The view hitherto taken of the starry heavens 
presents little that is new, since most of the constella- 
tions, visible in our latitude, and the most conspicuous 
of the individual stars, have been known from antiquity. 
But the objects to be described in the present chapter 
are chiefly such as have been discovered by modern 



306. Lesson I. Describe the appearance of the heavens for 
the middle of September from 8 to 10 o'clock. 

Lesson II. For the middle of December from 7 to 1 o'clock. 
Lesson III. For the middle of March from 8 to 10 o'clock. 
Lesson IV. For the middle of June from 9 to 10 o'clock. 



DOUBLE STARS. 265 

astronomy, aided by the powerful telescopes which, 
since the time of Sir William Herschel, have been 
directed to the heavens. Different orders and systems 
of stars have been brought to light, and a new and 
still more wonderful class of bodies, called Nebulae, 
have been reached in the depths of the stellar universe. 

308. The introduction into practical astronomy of 
Herschel's great Forty Feet Reflector, in 1789, was a 
grand event in the study of the stars. This instrument, 
in its previous humble forms, had been very little em- 
ployed upon the stars, they being supposed to be too 
remote for its powers, which seemed only suited to 
nearer worlds, as the sun and planets. It was not, how- 
ever, an increase of magnifying power that was wanted 
for researches on these distant objects, but an increase 
of light, by which a few scattered rays sent to us from 
bodies hidden in the depths of space, might be collected 
in such numbers, and directed into the eye, as would 
render visible objects otherwise invisible, not because 
they do not transmit to us any light, but because not 
enough of what they transmit enters the small pupil 
of the eye for the purposes of distinct vision. Tele- 
scopes of great aperture, therefore, by collecting a large 
beam of light and conveying it to the eye, greatly en- 
large the powers of this organ, and enabl,: it to pene- 
trate proportionally further into the most distant regions 
of the universe. Sir W. Herschel himself made won- 
derful progress in the knowledge of the starry heavens, 
and by his own researches discovered a large portion of 
those bodies which we are now to describe ; and his son, 
Sir John Herschel, has cultivated, with great success, 
the same field, and especially by a residence of five 
years at the Cape of Good Hope, devoted assiduously 
to observations with large instruments, has greatly 



307. What new objects present themselves in this chapter ? 
By what instrument have they been revealed to us ? 

23 



266 DOUBLE STARS. 

augmented our knowledge of the stellar systems of the 
southern hemisphere. Moreover, telescopes of still 
greater power than that of the elder Herschel, and es- 
pecially instruments capable of nicer angular measure- 
ments, have recently enriched the department of prac- 
tical astronomy. The most remarkable of these are the 
grand Reflector constructed by Lord Rosse, an Irish 
nobleman, and the great Refractors belonging respec- 
tively to the Pulkova and Cambridge Observatories. 
Lord Rosse's telescope considerably exceeds in dimen- 
sions and in power the forty feet reflector of Sir W. 
Herschel, being 50 feet in focal length, and having a 
diameter of 6 feet, whereas that of the Herschelian 
telescope was only 4 feet. This unexampled magnitude 
makes this instrument superior to all others in light, 
and fits it pre-eminently for observations on the most 
remote and obscure celestial objects, such as the faintest 
nebulae. But its unwieldy size, and its liability to loss 
of power, by the tarnishing or temporary blurring of 
the great speculum, will render it far less available for 
actual research than the great refractors which come in 
competition with it. Until recently, it was thought im- 
possible to form perfect achromatic object-glasses of 
more than about five inches diameter ; but they have 
been successively enlarged, until we can no longer set 
bounds to the dimensions which they may finally as- 
sume. The Pulkova telescope (at St. Petersburg) has 
a clear aperture of about 15 inches, and a focal length 
of 22 feet. The telescope recently acquired by Harvard 
University, is perhaps the finest refractor hitherto con- 
structed. It was made by the same artists, and upon 
the same scale with that, but its performances are 
thought even to exceed those of the Pulkova instru- 



308. What is said of Herschel's forty feet reflector? What 
is the peculiar advantage of such large telescopes ? Describe the 
Leviathan telescope of Lord Rosse, and those of Pulkova and 
Cambridge. 



DOUBLE STARS. 267 

ment. We now proceed to review some of the dis- 
coveries among the stars, which the researches made 
with such instruments as the foregoing have brought to 
light. 

309. Double Stars are those which appear single to 
the naked eye, but are resolved into two by the tele- 
scope ; or if not visible to the naked eye, are seen in 
the telescope very close together. Sometimes three or 
more stars are found in this near connection, constitu- 
ting triple or multiple stars. Castor, for example, when 

Castor. Pole-star. Triple. 



seen by the naked eye, appears as a single star ; but in 
a telescope, even of moderate powers, it is resolved into 
two stars, between the third and fourth magnitudes, 
within 5" of each other. These two stars are of nearly 
equal size, but frequently one is exceedingly small in 
comparison with the other, resembling a satellite near 
its primary, although in distance, in light, and in other 
characteristics, each has all the attributes of a star, and 
the combination, therefore, cannot be that of a planet 
with a satellite. 

When Sir William Herschel began his observa- 
tions on double stars, about the year 1780, he was 
acquainted with only 4. By his own researches he ex- 
tended the number to 2400. Sir John Herschel, Sir 
James South, and M. Struve, the great Russian astrono- 
mer, prosecuted the same line of research ; and when 
Sir John Herschel left England for the Cape of Good 
Hope, in 1833, the whole number of double stars en- 
rolled was 3346 ; and this number was increased, by 
that eminent astronomer, by adding those of the south- 
ern hemisphere, to 5542. The number of double stars 
is more than five thousand, and therefore considerably 



268 DOUBLE STARS. 

exceeds all the stars visible to the naked eye. In some 
instances, this proximity arises undoubtedly from the 
two members lying nearly in the same line of vision, 
and therefore being projected very near to each other on 
the face of the sky ; but in most cases the double stars 
are proved to have a physical relation to each other, 
and are therefore said to be physically double, while 
the former are said to be optically double. There is no 
longer any doubt that among the stars are separate 
systems, in which two, three, and even in one instance 
at least six stars are bound together in relations of 
mutual dependence, suns with suns, as the members of 
the solar system compose an individual province in the 
great empire of nature. A star in Orion's sword (Theta 
Orionis) has been for some time known as a quadruple 
star, the members of which form a small trapezium ; 
and recent observations have detected in two of these, 
severally, companions of extreme minuteness, the whole 
composing a figure like the following : 






Many of the double stars are distinguished by the 
components exhibiting different colors, often finely con- 
trasted with each other, as orange with blue or green, 
yellow with blue, and white with purple. Gamma 
Andromedse is a close double star, the components of 
which are both green. Insulated stars of a red color, 
almost as deep as that of blood, occur in many parts of 



309. What are Double Stars ? Give an example. With 
how many was Sir W. Herschel acquainted in 1780 ? State 
the successive additions, and the distinction between stars 
physically and optically double. Are there separate systems 
among the stars ? What is said of the quadruple star in 
Orion's Sword ? Are the double stars ever of different colors ? 



TEMPORARY STARS. 269 

the heavens, but no green or blue star of any decided 
hne has ever been noticed nnassociated with a compan- 
ion brighter than itself.* 

310. Temporary Stars are new stars which have sud- 
denly made their appearance, and, after a certain inter- 
val, as suddenly disappeared and returned no more. 
It was the appearance of a new star of this kind, 125 
years before the Christian era, that prompted Hippar- 
chus to form a catalogue of the stars, the first on record. 
Such also was the star which suddenly shone out, A. D. 
389, in the Eagle^ as bright as Venus, and after remain- 
ing three weeks, disappeared entirely. At other peri- 
ods, at distant intervals, similar phenomena have pre- 
sented themselves. Thus the appearance of a new star 
in 1572 was so sudden, that Tycho Brahe, returning 
home one evening, was surprised to find a collection 
of country people gazing at a star, which he was sure 
did not exist half an hour before. It was then as bright 
as Sirius, and continued to increase until it surpassed 
Jupiter when brightest, and was visible at midday. In 
a month it began to diminish, and in three months after- 
wards it had entirely disappeared. Some stars are now 
missing which were registered in the older catalogues. 
In one instance, at least (that of Neptune), the supposed 
star has proved to have been a planet. 

311. Variable Stars are those which undergo a 
periodical change of brightness. One of the most re- 
markable is the star Mira, in the neck of the Whale 
(Omicron Ceti). It appears once in 11 months, remains 
at its greatest brightness about a fortnight, being then, 
on some occasions, equal to a star of the second mag- 
nitude. It then decreases about three months, until it 
becomes completely invisible, and remains so about 



310. What are temporary stars? What led Hipparchus to 
form a catalogue of the stars ? Star discovered by Tycho. 



Herschel. 
23* 



270 VARIABLE STARS. 

five months, when it again becomes visible, and con- 
tinues increasing during the remaining three months of 
its period. 

Another very remarkable variable star is Algol 
{Beta Persei). It is suddenly visible as a star of the 
second magnitude, and continues such for 2d. 14h., 
when it begins rapidly to diminish in splendor, and in 
about 3^ hours is reduced to the fourth magnitude. It 
then begins again to increase, and in Z\ hours more, is 
restored to its usual brightness, going through all its 
changes in less than three days. This remarkable law 
of variation appears strongly to suggest the revolution 
round it of some opake body, which, when interposed 
between us and Algol, cuts off a large portion of its 
light. It is (says Sir J. Herschel) an indication of a 
high degree of activity in regions where, but for such 
evidence, we might conclude all to be lifeless. Our 
sun requires almost nine times this period to perform a 
revolution on its axis. On the other hand, the periodic 
time of an opake revolving body, sufficiently large, 
which would produce a similar temporary obscuration 
of the sun, seen from a fixed star, would be less than 
fourteen hours. 

The duration of these periods is extremely various. 
While that of Beta Persei, above mentioned, is less 
than three days, others are more than a year, and others 
many years. 

312. In various parts of the firmament are seen large 
groups, or clusters, which, either by the naked eye, or 
by the aid of the smallest telescope, are perceived to 
consist of a great number of small stars. Such are the 
Pleiades, Coma Berenices, and Prsesepe, or the Bee- 
hive, in Cancer. The Pleiades, or Seven Stars, as they 
are called, in the neck of Taurus, is the most conspicu- 



311. What are variable stars ? Give examples. What marks 
of activity do they indicate ? What is the duration of thes<j 
periodic variations ? 



NEBULAE. 271 

ous cluster. When we look directly at this group, we 
cannot distinguish more than six stars, but by turning 
the eye sideways* upon it, we discover that there are 
many more. The telescope only can, however, display 
the real magnificence of the Pleiades. Coma Bereni- 
ces has fewer stars, but they are of a larger class than 
those which compose the Pleiades. The Bee-hive, or 
Nebula of Cancer, is one of the finest objects of this 
kind for a small telescope, being, by its aid, converted 
into a rich congeries of shining points. A cluster in 
the sword-handle of Perseus, below Cassiopeia's chair, 
though but a dim speck to the naked eye, is a very ele- 
gant object to a large telescope, being separated into 
bright and beautiful stars, embracing several distinct 
subordinate clusters of exceedingly minute stellar points. 
The head of Orion affords an example of another cluster, 
though less remarkable than the others. 

313. Nebulae are faint misty objects seen in various 
parts of the firmament, always maintaining a fixed 
position, which resemble comets, or a speck of fog. 
The Galaxy, or Milky Way, presents a constant suc- 
cession of large nebulas. Of the individual nebulae, 
seen by the naked eye, the most conspicuous is that 
near the girdle of Andromeda. It is the oldest known 
nebula, having attracted the attention of star-gazers as 
early as the beginning of the tenth century, although 
it is commonly said to have been discovered by Simon 
Marius, in 1612. No powers of the telescope have 
been able to resolve this into separate stare, although 
the great Cambridge telescope reveals a vast number 
of stars, more than 1500, of various degrees of bright- 



312. What is said of clusters of stare? Give examples. 

* Indirect vision is far more delicate than direct. Tims we can see the 
Zodiacal Light or a comet's tail much more distinctly and better de- 
fined (partly, perhaps, by the effect of contrast), if we fix one eye on 
a part of the sky at some distance, and turn the other eye obliquely 
upon the object. 



272 



NEBULAE. 



ness, scattered over its surface ; but these appear not to 
belong to the nebula itself, which has hitherto afforded 
no evidence of resolution. Its dimensions are astonish- 
ingly great, since it covers a space of a quarter of a 
degree in diameter ; and we must bear in mind that, 
at such a distance as the fixed stars, a space of 15' im- 
plies an immense extent. Its figure is oval, and ellip- 
tical nebulae constitute a common variety among the 
figures which these bodies exhibit. Another very com- 
mon figure are the globular nebulae. A grand speci- 
men of this variety may be easily found in the constel- 
lation Hercules, between Zeta and Eta. Draw a line 
from Lyra to Gemma of the Crown, and 3° above the 
center of that line will be the place of this nebula. 
"When viewed with a small telescope, it exhibits only a 
globular cloud, but to a more powerful instrument it 
reveals its real glories in a form truly exciting to the 
beholder.* About 4000 nebulae have been detected and 
described, of which about 1700 have recently been 
added by Sir John Herschel, from his Eesults of Ob- 
servations at the Cape of Good Hope. Among the 
latter are two remarkable spots, well known to naviga- 
tors, situated near the south pole, called Magellanic 
Clouds by sailors, but by astronomers, the Nubecula 
Major and the Nubecula Minor. They are found to 
consist of a wonderful collection of nebulae, the greater 
embracing 278 nebulae, and the lesser 37. Both to- 
gether compose a most magnificent assemblage. In 
the sword of Orion is a celebrated nebula, long known, 
which, until recently, had resisted all attempts to re- 
solve it into stars ; but the great Reflector of Lord 
Rosse, and more recently the great Refractor of the 
Cambridge Observatory, have succeeded in a partial 
resolution, at least, of this grand object, and have 
authorized the anticipation that, with a small increase 
of telescopic power, the whole will be shown to consist 
of an immense collection of exceedingly minute stars. 

* See frontispiece. 



NEBUL-E. 273 

These great telescopes, by the superior light they 
afford, display their peculiar powers in this department 
of astronomy, and those astronomers who, for the first 
time, have gazed at these sidereal pictures as seen in 
the " Leviathan" of Lord Rosse, have expressed, in glow- 
ing terms, their mingled delight and astonishment. 
The perfect forms, and strange but symmetrical config- 
urations, exhibited by these instruments, of nebulse that 
were before seen of irregular or fantastic shapes, afford 
grounds for believing that such irregularities are often 
if not always owing to the objects being but partly de- 
veloped. Thus the Crab Nebula of Lord Rosse had 
been long known as a faint, ill-defined nebula of an 
elliptical shape ; but the higher powers of that instru- 
ment exhibit the before concealed appendages which 
are essential to the completeness of the figure. The 
Whirlpool Nebula of Rosse, when seen in separate 
parts, exhibited no signs of order or symmetry; but 
when viewed with the great Reflector, it develops the 
wonderful structure of a perfect spiral.* 

314. Nebulae were formerly divided into two classes, 
resolvable and irresolvable, the former term inrplying 
that the body was shown by the telescope to consist of 
stars, and the latter implying that the body is not com- 
posed of stars, but of a shining cloudy kind of matter 
diffused throughout the mass. Astronomers, at present, 
include all resolvable neublse under the head of clus- 
ters, appropriating the term nebulas exclusively to such 
of these bodies as have never been resolved. The 
question whether this distinction is not merely relative 
to the powers of the telescope, and whether, on the in- 



313. What are nebulae? What is said of the Milky Way? 
Of the nebula of Andromeda ? Of globular nebulae ? How 
many nebulas have been described ? W T hat is said of the Magel- 
lanic Clouds? -Of the nebula in Orion's Sword? How do the 
nebulae appear in great telescopes like that of Rosse ? 

* See frontispiece. 



274 xebulyE, 

crease of these powers, this class of bodies would not 
all be resolved into stars, is not easily determined, 
since the same increase of telescopic power which con- 
verts existing nebulae into clusters, brings to light a 
greater number of those which are irresolvable. 

These remote objects of the universe occasionally 
exhibit traces of that regard to beauty which every- 
where, in these nether worlds, characterizes the works 
of the Creator. In the Cross, a brilliant constellation 
of the southern hemisphere, for example, is a cluster 
surrounding the star Kappa Cruris, which consists of 
about 110 stars from the seventh magnitude down- 
wards, eight of the more conspicuous of which are 
colored with various shades of red, green, and blue, so 
as to give to the whole the appearance of a rich piece 
of jewelry. 

315. Nebulous stars are such as exhibit a sharp 
and brilliant star, surrounded by a disk or atmosphere 
of nebulous matter. These atmospheres, in some cases, 
present a circular, in others an oval figure ; and in 
certain instances, the nebula consists of a long, narrow, 
spindle-shaped ray, tapering away at both ends to 
points. Annular NebulcB (King-shaped) are among 
the rarest objects in the heavens. The most conspicu- 
ous of this class is in the Constellation Lyra, between 
the stars Beta and Gamma, about 6° S. E. of Alpha 
Lyres. This remarkable object is believed to be in fact 
a resolvable nebula or cluster, and yet the greatest 
powers of the telescope hitherto applied have only 
effected such changes as are regarded as giving signs 
of resolvability, but its perfect resolution has not been 
attained. Should it be achieved by an increased power 
of the instrument, astronomers look for a splendid coro- 



314. Point out the distinction between resolvable and irre- 
solvable nebulae. Are the figures of the nebulas ever beautiful ? 

315, What is said of nebulous stars? Of annular nebula; ? 



NEBULA. 275 

net of stars, more glorious, perhaps, than any thing 
hitherto discovered in the starry heavens. 

316. Planetary JVebulce constitute another variety, and 
are very remarkable objects. They have, as their name 
imports, exactly the appearance of planets. Whatever 
may be their nature, they must be of enormous magni- 
tude. One of them is to be found in the parallel of 
v Aquarii, and about 5m. preceding that star. Its appa- 
rent diameter is about 20". Another in the constella- 
tion Andromeda, presents a visible disk of 12", perfectly 
defined and round. Granting these objects to be equally 
distant from us with the stars, their real dimensions 
must be such as, on the lowest computation, would fill 
the orbit of Uranus. It is no less evident that, if they 
be solid bodies, of a solar nature, the intrinsic splendor 
of their surfaces must be almost infinitely inferior to 
that of the sun. A circular portion of the sun's disk, 
subtending an angle of 20", would give a light equal to 
100 full moons; while the objects in question are hardly, 
if at all, discernible with the naked eye.* 

317. The Milky Way, or Galaxy, is a well-known 
luminous zone, encircling the sphere nearly in the 
direction of a great circle. Near the Swan, in the 
northern sky, it is seen to be divided into two bands, 
which remain asunder for 150°, and then reunite. The 
Galaxy owes its peculiar appearance to the blended 
light of myriads of small stars too minute to be indi- 
vidually recognized by the naked eye, but which are 
seen in their true character by a telescope of only 
moderate powers. Sir William Herschel estimated that, 
on one occasion, in forty-one minutes, no less than 
258,000 stars passed through the small field of his tele- 



316. What is said of planetary nebulae? 

317. Describe the Milky Way or Galaxy. 

* Herschel. 



2*76 MOTIONS OF THE STARS. 

scope. In approaching the border of the Milky Way, 
there is found a regular but rapid increase in the num- 
ber of stars, even before entering the limits of the 
luminous zone itself. Sir J. Herschel computes the 
whole number of stars in the Milky Way at five and a 
half millions, including such only as are visible in his 
twenty feet reflector. The Galaxy is itself supposed 
to be a nebula, of which our sun with its planets 
forms a constituent part ; and it is thought that it ap- 
pears so much greater than other nebulae, only in con- 
sequence of our situation with respect to it, and its 
greater proximity to our svstem. 



CHAPTER III. 

MOTIONS OF THE FIXED STAES — DISTANCES NATUEE. 

318. In 1803, Sir William Herschel first determined 
and announced to the world, that there exist among the 
stars separate systems, composed of two stars, revolv- 
ing about each other in regular orbits. These he de- 
nominated Binary Stars, to distinguish them from 
other double stars where no such motion is detected, 
and whose proximity to each other may possibly arise 
from casual juxtaposition, or from one being in the 
range of the other. At present, more than a hundred 
of the binary stars are known, and as the number of 
such revolutions known among the double stars is con- 
stantly increasing as the times of comparison increase, 
it may be anticipated that, in after ages, so large a 
proportion of all the double stars will be found to pos- 
sess this character, as to authorize the belief that they 
universally consist of subordinate systems, of which 
the members have a revolution around a common 



318. What is said of binary stars ? Of their periodic times ? 



MOTIONS OF THE STARS. 277 

center of gravity. The periodic times of the binary 
stars are very various. While some (as Zeta Her cutis, 
and Eta Coronce) complete their revolutions in 30 or 40 
years, others (as Gam?na Virginis) require more than 
170, and others still (as 65 Piscium) take up the long 
period of 3000 years. 

319. The revolutions of the binary stars have assured 
us of this most interesting fact, that the law of gravita- 
tion extends to the fixed stars. Before these discoveries, 
we could not decide, except by a feeble analogy, that 
this law transcended the bounds of the solar system. 
Indeed, our belief of the fact rested more upon our 
idea of unity of design in all the works of the Creator, 
than upon any certain proof ; but the revolution of one 
star around another in obedience to forces which must 
be similar to those that govern the solar system, estab- 
lishes the grand conclusion, that the law of gravitation 
is truly the law of the material universe. 

We have the same evidence (says Sir John Herschel) 
of the revolutions of the binary stars about each other, 
that we have of those of Saturn and Uranus about the 
sun ; and the correspondence between their calculated 
and observed places in such elongated ellipses, must 
be admitted to carry with it a proof of the prevalence 
of the Newtonian law of gravity in their systems, of 
the very same nature and cogency as that of the calcu- 
lated and observed places of comets round the center 
of our own system. 

But (he acids) it is not with the revolutions of bodies 
of a planetary or cometary nature round a solar center 
that we are now concerned ; it is with that of sun around 
sun, each, perhaps, accompanied with its train of planets 
and their satellites, closely shrouded from our view by 
the splendor of their respective suns, and crowded into 



319. Of what interesting fact has the revolution of the binary 
stars assured us ? 

24 



278 MOTIONS OF THE STARS. 

a space, bearing hardly a greater proportion to the enor- 
mous interval .which separates them, than the distances 
of the satellites of our planets from their primaries, bear 
to their distances from the sun itself. 

320. Some of the fixed stars appear to have a Proper 
Motion, or a real motion in space. 

The apparent change of place in the stars arising 
from the precession of the equinoxes, has been already 
mentioned ; and several other sources of irregularity 
which give an apparent motion to the stars are well 
known ; but after all these corrections are made, 
changes of place still occur, which cannot result from 
any changes in the earth, but must arise from changes 
in the stars themselves. Such motions are called the 
proper motions of the stars. Nearly 2000 years ago, 
Hipparchus and Ptolemy made the most accurate de- 
terminations in their power of the relative situations of 
the stars, and their observations have been transmitted 
to us in Ptolemy's Almagest ; from which it appears 
that the stars retain at least very nearly the same places 
now as they did at that period. Still, the more accurate 
methods of modern astronomers have brought to light 
minute changes in the places of certain stars, which 
force upon us the conclusion, either that our solar sys- 
tem causes an apparent displacement of certain stars, 
by a motion of its own in space, or that they have thein- 
selves a proper motion. Possibly, indeed, both these 
causes may operate. 

321. If the sun, and of course the earth which ac- 
companies him, is actually in motion, the fact may 
become manifest from the apparent approach of the 
stars in the region which he is leaving, and the re- 
cession of those which lie in the part of the heavens 
towards which he is travelling. Were two groves of 
trees situated on a plain at some distance apart, and we 



320. What is said of the proper motion of the stars ? 



MOTIONS OF THE STARS. 2l9 

should go from one to the other, the trees before us 
would gradually appear further and further asunder, 
while those we left behind would appear to approach 
each other. Some years since, Sir William Herschel 
supposed he had detected changes of this kind among 
two sets of stars in opposite points of the heavens, and 
announced that the solar system was in motion towards 
a point in the constellation Hercules. As, for many 
years after this announcement, other astronomers failed 
to find evidence of such a motion of the solar system, 
the doctrine was generally discredited, until, within a 
few years, new and very refined researches have been 
instituted by several of the most eminent astronomers, 
which have fully confirmed the observations of Her- 
schel. The great Russian astronomer, Struve, by a 
comparison of the best observations, finds the exact 
point towards which the solar system is moving is in a 
line which joins the two stars Pi and Mu Herculis, — a 
point which can be easily found on the celestial globe, 
and thence transferred to the heavens. The researches 
of the younger Struve have conducted him to the 
velocity with which the solar system is moving in space, 
and he infers that the space through which the sun 
moves annually is 154,000,000 miles. Great as this 
space is, yet it may be remarked that it is only about 
one-fourth that traversed by the earth in its revolution 
around the sun. Within the comparatively short period 
during which these observations on the solar motion 
have been continued, the direction appears rectilinear ; 
but all analogy leads to the belief that it is in fact a 
motion of revolution, although, on account of the im- 
mense size of the orbit, and, consequently, its small 
curvature, many years will be requisite in order to 
determine the deviation from the line of the tangent. 

322. When we reflect on the immense distance of 



321. How is the motion of the sun in space indicated 
Towards what constellation is it moving ? 



280 MOTIONS OF THE STARS. 

the stars, we may readily believe that they may be in 
fact in rapid motion, and yet appear quiescent ; as a 
distant ship, under full sail, appears at rest, although 
actually moving at the rate of ten knots an hour. Thus 
it is found that a motion of the sun in space, so 
seen from the nearest fixed stars, would make it de- 
scribe an arc of only about one-third of a second 
annually, although traversing a space of 154 millions 
of miles. But a small change in the place of a star in 
a single year may, in a long series of years, accumulate 
to a very sensible amount. For example, the latitudes 
of the three bright stars, Sirius, Arcturus, and Alde- 
baran, were determined by Hipparchus 130 years be- 
fore the Christian era, and their assigned places are 
transmitted to us in the Almagest of Ptolemy. About 
the year 1700, Dr. Halley found that these stars had, 
during the interval of nearly 2000 years, moved 
southerly through the spaces respectively of 37', 42', 
and 33'. The immense pains that have of late years 
been bestowed upon catalogues of the stars, and es- 
pecially of particular portions of the heavens, with the 
view of furnishing, to after ages, the most accurate 
data for comparison, will enable future astronomers to 
study the proper motions of the stars with far greater 
advantages than the present generation enjoys. In 
most cases where a proper motion in certain stars has 
been suspected, its annual amount has been so small, 
that many years are required to assure us that the effect 
is not owing to some other than a real progressive mo- 
tion in the stars themselves ; but in a few instances the 
fact is too obvious to admit of any doubt. A greater 
proportion of the double stars than of any other in- 
dicate proper motions, especially the binary stars, or 
those which have a revolution around each other. 



322. How may a star be in rapid motion, and yet appear 
nearly at rest ? Through what space does the sun move an- 
nually? What class of stars Lave the greatest proper motion? 



DISTANCES OF THE STARS. 281 



DISTANCES OF THE FIXED STAKS. 

323. It has long been considered one of the highest 
problems that can be proposed to the human mind, to 
measure the distance to any of the fixed stars. Noth- 
ing more, indeed, would be necessary than to determine 
its horizontal parallax ; but this is so exceedingly small, 
that, until recently, all efforts to measure it had proved 
unavailing. For all measurements relating to the dis- 
tances of the sun and planets, the diameter of the earth 
furnishes the base line. The length of this line being- 
known, and likewise the horizontal parallax of the body 
whose distance is sought, we readily obtain the distance 
by the solution of a right-angled triangle. But any 
star viewed from the opposite sides of the earth, would 
appear from both stations to occupy precisely the same 
situation in the celestial sphere, and of course it would 
exhibit no horizontal parallax. But astronomers have 
endeavored to find a parallax in some of the fixed stars, 
by taking the diameter of the earth's orbit as a base 
line. Yet even a change of position amounting to 190 
millions of miles, has, until within a few years, proved 
insufficient to alter the apparent place of a single fixed 
star, from which it was concluded that the fixed stars 
have not even any annual parallax ; or that the angle 
subtended by the semidiameter of the earth's orbit, at 
the nearest fixed star, is insensible. The errors to which 
instrumental measurements are subject, are such, that 
the angular determinations of celestial arcs, it was 
supposed, could not be relied on to less than 1" ; and 
the change of place in any star that had been examined 
for parallax being less than one second when viewed at 
opposite extremities of the earth's orbit, the conclusion 
was, that the parallax of the fixed stars, if any exist, is 
too minute ever to be measured by instruments. 

After many fruitless and delusory efforts to meas- 
ure the immense interval that separates us from 
the fixed stars, the great Prussian astronomer, Bessel, 

24* 



282 DISTANCES OF THE STARS. 

in the year 1838, determined this interesting and im- 
portant element, by observations on a double star in the 
Swan (61 Cygni). This star was selected for the fol- 
lowing reasons : first, it was known to have a great 
proper motion, indicating a comparatively great prox- 
imity to our system ; secondly, situated as it is among 
the circumpolar stars, observations could be made 
upon it nearly every night in the year ; and, thirdly, 
the great number of small stars in the immediate 
neighborhood, furnished the opportunity of select- 
ing favorable stationary points from which (inasmuch 
as these more remote objects might be considered as 
entirely devoid of parallax) any changes of place in 
the nearer, in consequence of an annual parallax, might 
be readily estimated. By observations of the last de- 
gree of refinement, conducted for a period of several 
years, a parallax was decisively indicated, amounting 
to about one-third of a second ; or, more exactly, to 
0."3183, implying a distance of 592,200 times the mean 
distance of the earth from the sun, or a space which it 
would take light, moving at the rate of twelve millions 
of miles per minute, nine and a quarter years to 
traverse. To form some familiar notions of this dis- 
tance, let us suppose a railway-car to travel night and 
day, at the rate of twenty miles an hour : we should 
find it would take it about 517 years to reach the sun ; 
but to reach 61 Cygni would require 324,000,000 of 
years. 

324. The observations of Bessel enabled him to es- 
timate also the period of revolution of the two stars 



323. What has been long considered one of the greatest of 
problems ? What element must be first determined before we 
can measure the distance of a fixed star ? What is used as a 
base line ? What is said of the minuteness of the annual 
parallax, and of the discovery of that of 6 1 Cygni ? What is 
the amount of this parallax ? How long would it take light to 
traverse the distance ? How long a rail-car ? 



DISTANCES OF THE STAES. 283 

composing the binary system of 61 Cygni, and the 
dimensions of the orbit, and he found the periodic time 
about 540 years, and the length of the orbit about two 
and a half times that of Uranus. Knowing also the 
distance of this star, we can now determine from its 
proper motion (five seconds a year) the velocity of its 
motion : this is found to be about forty-four miles per 
second — more than double that of the earth in its orbit 
— amounting to about one thousand millions of miles 
per annum. 

On account of the smallness of the supposed parallax 
thus found, it would not be unreasonable still to enter- 
tain a lingering suspicion, that it is nothing more than 
the unavoidable imperfection of instrumental measure- 
ments, as proved to be the case in previous attempts to 
find the same element ; but the most satisfactory evi- 
dence which the world can have that such is not the 
fact in the present instance, but that the parallax is 
truly found, is that the most celebrated astronomers of 
the age, after rigorous scrutiny, have acknowledged the 
reality and soundness of the determination. Our con- 
fidence that the parallax of 61 Cygni was truly deter- 
mined by Bessel, is strengthened by the fact that a 
separate determination recently made by Peters at the 
Pulkova Observatory, gives almost precisely the same 
result, that of Bessel being 0."318, and that of Peters 
0."349. In the case of several stars still more distant, 
the parallax has been found, with more or less proba- 
bility, but with sufficient to command the general con- 
fidence of astronomers. Thus, the parallax of Arcturus, 
Alpha Lyrse, and Polaris, were also found bv Peters to 
be respectively 0/127, 0/123, 0."067, that of the Pole- 



324. What is the peiiodic time of the stars composing the 
binary system of 61 Cygni, and the length of orbit ? "What is 
said of the evidence attending these results ? Also of the 
parallax of Arcturus, Alpha Lyrse, the Pole-star, and Alpha 

Centauri \ 



284 NATURE OF THE STARS. 

star being only one-fifth as great as that of 61 Cygni ; 
and, consequently, if light would require 9 \ years to 
come from that star, it would require more than 46 
years to come to us from the Pole-star. A star in the 
southern hemisphere, (Alpha Centauri,) indicates a 
parallax of about 1", and hence appears at present the 
nearest of the fixed stars. 

MATURE OF THE STARS. 

325. The stars are bodies greater than our earth. If 
this were not the case they could not be visible at such 
an immense distance. Dr. Wollaston, a distinguished 
English philosopher, attempted to estimate the magni- 
tudes of certain of the fixed stars from the light which 
they afford. By means of an accurate photometer (an 
instrument for measuring the relative intensities of 
light) he compared the light of Sirius with that of the 
sun. He next inquired how far the sun must be re- 
moved from us in order to appear no brighter than 
Sirius. He found the distance to be 141,400 times its 
present distance. But Sirius is more than 200,000 times 
as far off as the sun. Hence he inferred that, upon the 
lowest computation, Sirius must actually give out twice 
as much light as the sun. Indeed, he has rendered it 
probable that the light of Sirius is equal to fourteen suns. 
From the smallness of its parallax it is inferred to be 
equal to sixty-three suns. 

326. The fixed stars are suns. We have already 
seen that they are large bodies ; that they are immensely 
further off than the furtherest planet ; that they shine 
by their own light, as is evident by the nature of the 
light as tested by polarization : in short, that their ap- 
pearance is, in all respects, the same as the sun would 



325. What evidence have we that the Stars are greater than 
the Earth ? Also that they are Suns ? How much larger is 
Sirius than the Sun ? 



SYSTEM OF THE WORLD. 285 

exhibit if removed to the region of the stars. Hence 
we infer that they are bodies of the same kind with 
the sun. 

We are justified therefore by a sound analogy, in 
concluding that the stars were made for the same end 
as the sun, namely, as the centers of attraction to other 
planetary worlds, to which they severally dispense light 
and heat. Although the starry heavens present, in a 
clear night, a spectacle of ineffable grandeur and 
beauty, yet it must be admitted that the chief purpose 
of the stars could not have been to adorn the night, 
since by far the greatest part of them are wholly in- 
visible to the naked eye ; nor as landmarks to the 
navigator, for only a very small proportion of them are 
adapted for this purpose ; nor, finally, to influence the 
earth by their attractions, since their distance renders 
such an effect entirely insensible. If they are suns, 
and if they exert no important agencies upon our 
world, but are bodies evidently adapted to the same 
purpose as our sun, then it is as rational to suppose 
that they were made to give light and heat, as that the 
eye was made for seeing and the ear for hearing. It 
is obvious to inquire next, to what they dispense these 
gifts if not to planetary worlds ; and why to planetary 
worlds, if not for the use of percipient beings ? We 
are thus led, almost inevitably, to the idea of a Plu- 
rality of Worlds ; and the conclusion is forced upon 
us, that the spot which the Creator has assigned to us 
is but a humble province of his boundless empire. 

SYSTEM OF THE WORLD. 

327. The arrangement of all the bodies that compose 
the material universe, and their relations to each other, 
constitute the System of the World. 

In the earliest ages of the world mankind believed 
that the earth was an extended plane, at rest in the 



326. For what purpose were the stars created ? 



286 SYSTEM OF THE WORLD. 

center of the "universe, and that all the heavenly bodies 
daily revolved around it. The ancient Greek astrono- 
mers, however, taught that the earth is round, and one 
of the most celebrated of them, Pythagoras, even went 
so far as to maintain that the sun is the true center 
around which the earth and planets resolve. But this 
opinion found hardly any supporters, until it was re- 
vived and matured into a system by Copernicus, a 
Prussian astronomer, not far from the year 1500. It is 
now universally regarded by astronomers as the true 
view of the mechanism of the solar system. 

The Copemican System, as was briefly mentioned 
near the beginning of this work, maintains (1), That the 
apparent diurnal revolution of the heavenly bodies, 
from east to west, is owing to the real revolution of the 
earth on its own axis from west to east, in the same 
time ; and (2), That the sun is the center around which 
the earth and planets all revolve from west to east, con- 
trary to the opinion that the earth is the center of motion 
of the sun and planets. 

Pirst, the earth revolves on its axis. 

1. This supposition is vastly more simple, than that 
the whole host of heaven, sun, planets, and stars, in- 
cluding millions of bodies larger than the earth, is all 
carried daily around our little planet. 

2. The velocity which such a daily circuit would im- 
ply, especially in the fixed stars, is wholly incredible. 

3. Such a revolution of the earth is agreeable to 
analogy, since the other planets are seen, by the tele- 
scope, to turn on their axes. 

4. The sp>heroidal figure of the earth, and the dimin- 
ished tveight of bodies at the equator, are the natural 
effects of such a revolution. 

Secondly, the planets, including the earth, revolve 
about the sun. 

1. The phases and motions of Mercitry and Venus 
are precisely such as would result from their revolving 
about the sun in orbits within that of the earth, and in- 
consistent with any other supposition. 



SYSTEM OF THE WORLD. 287 



2. The superior planets are found by actual measure- 
ment always to keep at nearly the same distance from 
the sun, and therefore they revolve around the sun as a 
center. 

3. The earth itself also is proved by the most con- 
clusive arguments to revolve around the sun, and not 
the sun around the earth. For the sun being vastly 
larger and heavier than the earth, its centrifugal force 
would be greater than could be balanced by the earth's 
attraction, and would carry it away from the earth into 
space, drawing the earth after it. 

Thirdly, Since it is known that the laws of the plane- 
tary system, namely, the law of gravitation and Kep- 
ler's laws, extend to the stars, and that some of them, 
as the Binary stars, are bound together in systems 
similar to the solar system, and that many other stars 
are seen to be in motion ; the most rational conclusion 
is, that there exist multitudes of starry systems, con- 
structed upon the same model as the planetary system, 
and, finally, that all these subordinate systems of worlds 
are combined under the same mechanical laws to form 
the grand machine of the Universe. 



32*7. Define the term system of the world. What opinions 
prevailed respecting it in the earliest ages ? What among the 
ancient Greek astronomers ? What are the two leading points 
of the Copernican system ? How is it proved that the earth 
turns on its axis ? How that it revolves about the sun ? What 
higher systems are supposed to exist ? How are these combined 
to form the Universe ? 



VALUABLE WORKS 

PUBLISHED BY 

ROBERT B. COLLINS, 

TCo. 254 frtfl Sfireef, fob J|ori|. 



PROFESSOR OLMSTED'S SERIES. 

OLMSTED'S NATURAL PHILOSOPHY. 8vo. College 
edition. 

An Introduction to Natural Philosophy ; designed as a text- 
book for students in Yale College. 

OLMSTED'S ASTRONOMY. 8vo. College edition. 

An Introduction to Astronomy ; designed as a text-book for the 
use of students in Yale College. 

The two works were originally prepared by the author (Denison 
Olmsted, L.L.D.) for the use of the classes under his care in Yale 
College, and have been adopted as text-books in most of the col- 
leges and higher seminaries of learning in the country. 

MASON'S SUPPLEMENT. 

An Introduction to Practical Astronomy, designed as a Supple- 
ment to Olmsted's Astronomy ; containing Special Rules for the 
Adjustment and Use of Astronomical Instruments, together with 
the Calculation of Eclipses and Occupations, and the method of 
finding the Latitude and Longitude. By Ebenezer Porter Mason. 

OLMSTED'S SCHOOL ASTRONOMY. 12mo. 

A Compendium of Astronomy ; containing the Elements of the 
Science familiarly explained and illustrated, with the Latest Dis- 
coveries, for the use of schools and academies and of the general 
reader. 

OLMSTED'S RUDIMENTS. l8mo. 

Rudiments of Natural Philosophy and Astronomy ; designed for 
the younger classes in academies and for common schools. A very 
valuable text-book for beginners. 



ROBERT B. COLLINS'S PUBLICATIONS. 



PROFESSOR COFFIN'S WORKS. 

COFFIN'S ECLIPSES. 

Solar and Lunar Eclipses, Familiarly Illustrated and Explained, 
with the Method of Calculating them according to the Theory of 
Astronomy, as taught in the New England Colleges. 

COFFIN'S CONIC SECTIONS. 

Elements of Conic Sections and Analytical Geometry. 

These works, by Prof. James H. Coffin, of Lafayette College, Pa., 
have received the highest recommendations from qualified author- 
ity. Of the second named, (Conic Sections, (fee.) Prof. Loomis, 
(College of New Jersey,) Prof. Sadler, Prof. Mason, and other dis- 
tinguished gentlemen, unite in approval. 



BY LYMAN PRESTON. 

PRESTON'S DISTRICT SCHOOL BOOK-KEEPING, 

Affording an interesting and profitable exercise for youth, being 
especially designed for Classes in our Common Schools. 

PRESTON'S BOOK-KEEPING BY SINGLE ENTRY, 

Adapted to the use of Retailers, Farmers, Mechanics, and Common 
Schools. 

PRESTON'S TREATISE ON BOOK-KEEPING ; 

A common-sense guide to a common-sense mind. In two parts — 
the first the Single Entry method, the second being arranged more 
particularly for the instruction of young men who contemplate 
the pursuit of mercantile business, showing the method of keeping 
accounts by Double Entry, and embracing a variety of useful forms. 
This is the most popular work upon the subject, and is in very 
extensive use throughout the country. 



ADAMS'S ARITHMETICAL SERIES. 
ADAMS'S PRIMARY ARITHMETIC, 

Or Mental Operationsin Numbers, an Introduction to Adams's New 
Arithmetic, revised edition. An excellent work for young learners. 

ADAMS'S NEW ARITHMETIC. Revised edition. 

By Daniel Adams, M.D. A new edition of this superior work, 
with various improvements and additions, as the wants of the 
times demand. A Key is published separately. 

ADAMS'S MENSURATION, MECHANICAL POWERS, 
AND MACHINERY. 

This admirable work is designed as a senuel to the Arithmetic. 



ROBERT B. COLLINS'S PUBLICATIONS. 



ADAMS'S BOOK-KEEPING. 

A Treatise on Book-keeping by Single Entry, accompanied b 
blanks for the use of learners. 



ABBOTT'S SERIES. 

ABBOTT'S HEADERS. 

The Mount Yernon Reader for Junior Classes. 18mo 
The Mount Vernon Reader for Middle Classes. 18mo. 
The Mount Vernon Reader for Senior Classes. 12mo. 

ABBOTT'S FIRST ARITHMETIC. 

The Mount Vernon Arithmetic. Part First : Elementary. 
The Mount Vernon Arithmetic. Part Second : Fractions. 

ABBOTT'S ABERCROMBIE'S PHILOSOPHY. 

Inquiries concerning the Intellectual Powers and the Investiga- 
tion of Truth. By John Abercrombie, M.D. F.R.S. Edited, with 
additions, by Jacob Abbott. 

The Philosophy of the Moral Feelings. By John Abercrombie. 
Edited by Jacob Abbott. 

ABBOTT'S DRAWING CARDS. 

In three Sets, 40 Cards to each. 



WHELPLEY'S COMPEND OF HISTORY. 

With Questions by Joseph Emerson. 12mo. 

BADLAM'S WRITING BOOKS. 

The Common School "Writing Books. A New Series of Nine 
Numbers. By Otis GL Badlam. 

ADDICK'S ELEMENTS 
OF THE FRENCH LANGUAGE 

An excellent elementary work. 

GIRARD'S ELEMENTS 
OF THE SPANISH LANGUAGE. 

A. practical work to Teach, to Speak, and "Write Spanish. By 
J. F. Girard. 

. KIRKHAM'S GRAMMAR. 

English Grammar in Familiar Lectures, for the Use of Schools. 
By Samuel Kirkham. The work is very extensively used. 

DAY'S MATHEMATICS. 
A Treatise for Students, by President Day, of Yale College. 



ROBERT B. COLLINS'S PUBLICATIONS. 

THE GOVERNMENTAL INSTRUCTOR. 

A Brief and Comprehensive View of the Government of the 
United States, and of the State Governments, in easy lessons, for 
the use of Schools. By J. B. Shurtleff. 

THE OXFORD DRAWING-BOOK. 

Containing Progressive Lessons on Sketching, Drawing and 
Coloring Landscape Scenery, Animals and the Human Figure. 
With 100 Lithographic Drawings. 4to. 

JOHN RUBENS SMITH'S DRAWING-BOOK. 

The Rudiments of the Art explained in Easy Progressive Les- 
sons, embracing Drawing and Shading. With numerous Copper- 
plate Engravings. 

STUDIES IN FLOWER PAINTING. 
By Jas. Andrews. Colored plates. 

DYMOND'S ESSAYS. 

On the Principles of Morality, and the Private and Political 
Rights and Obligations of Mankind. By J. Dymond. 

KEMPIS. 

The Imitation of Christ. By Thomas a Kempis. Translated 
by John Payne, with Introductory Essay by Thomas Chalmers. 

jESOP'S fables. 

A New Version, by Rev. Thomas James. Illustrated by James 
Tenniel. The best edition published in the country. 

OUR COUSINS IN OHIO. 
By Mary Howitt. From the Diary of an American Mother. 1 8uao„ 

GABRIEL. 
A Story of Wichnor Wood. By Mary Howitt, 

THE AMERICAN SCHOOL PRIMER. 
Illustrated. 46 pp., 12mo. 

THE CHILD'S PRIMER. 
Illustrated. 36 pp., 18mo. 

JOHN WOOLMAN'S JOURNAL. 

DAVID SANDS' JOURNAL. 

THE NEW TESTAMENT. 
8vo. Large print. 




003 630 374 



